Publishing type：Research paper (scientific journal)  

© 2019 American Physical Society. In the previous paper [Harada, Cardoso, and Miyata, Phys. Rev. D 99 (2019), 044039PRVDAQ2470-001010.1103/PhysRevD.99.044039], it is shown that a hollow transmissive shell collapsing to an ultracompact object of radius very close to its horizon radius generally emits transient Hawking radiation (THR) followed by a couple of bursts separated from each other by a long time interval. In the current paper, we expand the previous work in two independent directions: changing boundary conditions and specifying the equations of state (EOSs) of the matter. First, we introduce a perfectly reflective surface collapsing to an ultracompact object and find that this model also emits THR that is followed only by a single burst. Second, we introduce two different collapse dynamics to an ultracompact object and specify the corresponding matter EOSs. We find that THR is quite commonly seen in early times, while the subsequent bursts strongly depend on the boundary condition and the EOS or the braking behavior of the surface.

DOI： 10.1103/PhysRevD.100.084028

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© 2019 American Physical Society. Stability of a photon sphere, or stability of circular null geodesics on the sphere, plays a key role in its applications to astrophysics. For instance, an unstable photon sphere is responsible for determining the size of a black hole shadow, while a stable photon sphere is inferred to cause the instability of spacetime due to the trapping of gravitational waves on the radius. A photon surface is a geometrical structure first introduced by Claudel, Virbhadra, and Ellis as the generalization of a photon sphere. The surface does not require any symmetry of spacetime and has its second fundamental form of pure trace. In this paper, we define the stability of null geodesics on a photon surface. It represents whether null geodesics perturbed from the photon surface are attracted to or repelled from the photon surface. Then, we define a strictly (un)stable photon surface as a photon surface on which all null geodesics are (un)stable. We find that the stability is determined by Riemann curvature. Furthermore, it is characterized by the normal derivative of the second fundamental form. As a consequence, for example, a strictly unstable photon surface requires nonvanishing Weyl curvature on it if the null energy condition is satisfied.

DOI： 10.1103/PhysRevD.100.064040

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© 2019 American Physical Society. In the 12th line of the Abstract, the prefactor 1.9 x 10-6 in the estimate of should be replaced with 1.9 x 10-7. The prefactor 1.894 x 10-6 in both Eq. (5.8) and the upper line of Eq. (5.10) should be replaced with 1.921 x 10-7. No result is affected except the above correction. The authors thank Tommi Tenkanen and Takahiro Terada for bringing this point to the their attention.

DOI： 10.1103/PhysRevD.99.069904

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© 2019 American Physical Society. Any observer outside black holes cannot detect any physical signal produced by the black holes themselves, since, by definition, the black holes are not located in the causal past of the outside observer. In fact, what we regard as black hole candidates in our view are not black holes but will be gravitationally contracting objects. As well known, a black hole will form by a gravitationally collapsing object in the infinite future in the views of distant observers like us. At the very late stage of the gravitational collapse, the gravitationally contracting object behaves as a blackbody due to its gravity. Due to this behavior, the physical signals produced around it (e.g., the quasinormal ringings and the shadow image) will be very similar to those caused in the eternal black hole spacetime. However, those physical signals do not necessarily imply the formation of a black hole in the future, since we cannot rule out the possibility that the formation of the black hole is prevented by some unexpected event in the future yet unobserved. As such an example, we propose a scenario in which the final state of the gravitationally contracting spherical thin shell is a gravastar that has been proposed as a final configuration alternative to a black hole by Mazur and Mottola. This scenario implies that time necessary to observe the moment of the gravastar formation can be much longer than the lifetime of the present civilization, although such a scenario seems to be possible only if the dominant energy condition is largely violated.

DOI： 10.1103/PhysRevD.99.044027

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© 2019 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the »https://creativecommons.org/licenses/by/4.0/» Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Black holes (BHs) play a central role in physics. However, gathering observational evidence for their existence is a notoriously difficult task. Current strategies to quantify the evidence for BHs all boil down to looking for signs of highly compact, horizonless bodies. Here, we study particle creation by objects which collapse to form ultracompact configurations, with the surface at an areal radius R=Rf satisfying 1-(2M/Rf)=ϵ21 with M the object mass. We assume that gravitational collapse proceeds in a "standard" manner until R=Rf+2Mϵ2β, where β>0, and then slows down to form a static object of radius Rf. In the standard collapsing phase, Hawking-like thermal radiation is emitted, which is as strong as the Hawking radiation of a BH with the same mass but lasts only for ∼40(M/M)[44+ln(10-19/ϵ)] μs. Thereafter, in a very large class of models, there exist two bursts of radiation separated by a very long dormant stage. The first burst occurs at the end of the transient Hawking radiation and is followed by a quiescent stage which lasts for ∼6×106(ϵ/10-19)-1(M/M) yr. Afterwards, the second burst is triggered, after which there is no more particle production and the star is forever dark. In a model with β=1, both the first and second bursts outpower the transient Hawking radiation by a factor ∼1038(ϵ/10-19)-2.

DOI： 10.1103/PhysRevD.99.044039

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Language：English   Publishing type：Research paper (scientific journal)  

© The Author(s) 2018. Published by Oxford University Press on behalf of the Physical Society of Japan. The production rate of primordial black holes (PBHs) is often calculated by considering a nearly Gaussian distribution of cosmological perturbations, and assuming that black holes will form in regions where the amplitude of such perturbations exceeds a certain threshold. A threshold ζth for the curvature perturbation is somewhat inappropriate for this purpose, because it depends significantly on environmental effects, not essential to the local dynamics. By contrast, a threshold δth for the density perturbation at horizon crossing seems to provide a more robust criterion. On the other hand, the density perturbation is known to be bounded above by a maximum limit δmax at the horizon entry and, given that δth is comparable to δmax, the density perturbation will be far from Gaussian near or above the threshold. In this paper, we provide a new plausible estimate for the primordial black hole abundance based on peak theory. In our approach, we assume that the curvature perturbation is given as a random Gaussian field with the power spectrum characterized by a single scale, while an optimized criterion for PBH formation is imposed, based on the locally averaged density perturbation around the nearly spherically symmetric high peaks. Both variables are related by the full non-linear expression derived in the long-wavelength approximation of general relativity. We do not introduce a window function, which is usually introduced to obtain the scale dependence of the spectrum. The scale of the inhomogeneity is introduced as a random variable in the peak theory, and the scale-dependent PBH fraction is automatically induced. We find that the mass spectrum is shifted to larger mass scales by one order of magnitude or so, compared to a conventional calculation. The abundance of PBHs becomes significantly larger than the conventional one, by many orders of magnitude, mainly due to the optimized criterion for PBH formation and the removal of the suppression associated with a window function.

DOI： 10.1093/ptep/pty120

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society  

© 2018 American Physical Society. A strong gravity naked singular region can give important clues toward understanding the classical as well as spontaneous nature of General Relativity. We propose here a model for energy emission from a naked singular region in a self-similar dust spacetime by gluing two self-similar dust solutions at the Cauchy horizon. The energy is defined and evaluated as a surface energy of a null hypersurface, the null shell. Also included are scenarios of the spontaneous creation or disappearance of a singularity, the end of inflation, black hole formation, and bubble nucleation. Our examples investigated here explicitly show that one can model unlimitedly luminous and energetic objects in the framework of General Relativity.

DOI： 10.1103/PhysRevD.97.104014

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier B.V.  

© 2018 The Author(s) The superspinar proposed by Gimon and Hořava is a rapidly rotating compact entity whose exterior is described by the over-spinning Kerr geometry. The compact entity itself is expected to be governed by superstringy effects, and in astrophysical scenarios it can give rise to interesting observable phenomena. Earlier it was suggested that the superspinar may not be stable but we point out here that this does not necessarily follow from earlier studies. We show, by analytically treating the Teukolsky equations by Detwiler's method, that in fact there are infinitely many boundary conditions that make the superspinar stable at least against the linear perturbations of m=l modes, and that the modes will decay in time. Further consideration leads us to the conclusion that it is possible to set the inverse problem to the linear stability issue: since the radial Teukolsky equation for the superspinar has no singular point on the real axis, we obtain regular solutions to the Teukolsky equation for arbitrary discrete frequency spectrum of the quasi-normal modes (no incoming waves) and the boundary conditions at the “surface” of the superspinar are found from obtained solutions. It follows that we need to know more on the physical nature of the superspinar in order to decide on its stability in physical reality.

DOI： 10.1016/j.physletb.2018.03.014

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Institute of Physics Publishing  

We completely classify Friedmann-Lemaĩtre-Robertson-Walker solutions with spatial curvature K = 0,±1 and equation of state p = wρ, according to their conformal structure, singularities and trapping horizons. We do not assume any energy conditions and allow φ &lt
0, thereby going beyond the usual well-known solutions. For each spatial curvature, there is an initial spacelike big-bang singularity for w &gt
-1/3 and ρ &gt
0, while there is no bigbang singularity for w &lt
-1 and ρ &gt
0. For K = 0 or -1, -1 &lt
w &lt
-1/3 and ρ &gt
0, there is an initial null big-bang singularity. For each spatial curvature, there is a final spacelike future big-rip singularity for w &lt
-1 and ρ &gt
0, with null geodesics being future complete for -5/3 ≤ w &lt
-1 but incomplete for w &lt
-5/3. For w = -1/3, the expansion speed is constant. For -1 &lt
w &lt
-1/3 and K = 1, the universe contracts from infinity, then bounces and expands back to infinity. For K = 0, the past boundary consists of timelike infinity and a regular null hypersurface for -5/3 &lt
w &lt
-1, while it consists of past timelike and past null infinities for w ρ -5/3. For w &lt
-1 and K = 1, the spacetime contracts from an initial spacelike past bigrip singularity, then bounces and blows up at a final spacelike future big-rip singularity. For w &lt
-1 and K = -1, the past boundary consists of a regular null hypersurface. The trapping horizons are timelike, null and spacelike for w ϵ (-1, 1/3), w ϵ {1/3,-1} and w ϵ
(-∞,-1) ∪ (1/3,∞), respectively. A negative energy density (ρ &lt
0) is possible only for K = -1. In this case, for w &gt
-1/3, the universe contracts from infinity, then bounces and expands to infinity
for -1 &lt
w &lt
-1/3, it starts from a big-bang singularity and contracts to a big-crunch singularity
for w &lt
-1, it expands from a regular null hypersurface and contracts to another regular null hypersurface.

DOI： 10.1088/1361-6382/aab99f

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Publishing type：Research paper (international conference proceedings)  

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Language：English   Publishing type：Research paper (international conference proceedings)  

© Proceedings of the 28th Workshop on General Relativity and Gravitation in Japan, JGRG 2018. All rights reserved. Accretion problem: Rotational flow in spherically symmetric spacetime of D-dim. Dynamical system analysis. SP/PS correspondence: Theorem (SP/PS correspondence) For our accretion model, for any stationary and axially symmetric physical transonic accretion flow of radiation fluid, its sonic point is located at (one of) the unstable photon sphere(s). Discussions The physical reason? In other cases? e.g. spacetime of different symmetries (in progress).

DOI： 10.1103/PhysRevD.98.024018

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Publishing type：Research paper (international conference proceedings)  

© Proceedings of the 28th Workshop on General Relativity and Gravitation in Japan, JGRG 2018. All rights reserved. The Vlasov matter reduces to a perfect fluid if the distribution function is isotropic in momentum space. A static solution of the Einstein-Vlasov system with isotropic distribution function is necessarily spherically symmetric and unique for a given surface potential provided that the pressure is sufficiently low and the energy cutoff of the distribution function is not too smooth. For a shallow potential and isotropic distribution function F(E) with F = 0 for E > E0 and F ≃ C(E0 − E)n near the cutoff E0, the EOS becomes polytropic. The uniqueness holds for 0 ≤ n < 7/2. We analytically and numerically investigated the case of a step-function distribution. There exists a unique spherically symmetric static solution for a shallow potential, while the uniquness may break down if the regime of a deep potential is included.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Angular momentum plays very important roles in the formation of primordial black holes in the matter-dominated phase of the Universe if it lasts sufficiently long. In fact, most collapsing masses are bounced back due to centrifugal force, since angular momentum significantly grows before collapse. For masses with q &lt;= q(c) similar or equal to 2.4I(1/3)sigma(1/3)(H), where q is a nondimensional initial quadrupole moment parameter, sigma(H) is the density fluctuation at horizon entry t = t(H), and I is a parameter of the order of unity, angular momentum gives a suppression factor similar to exp (-0.15I(4/3)sigma(-2/3)(H)) to the production rate. As for masses with q &gt; q(c), the suppression factor is even stronger as similar to exp(-0.0046q(4)/sigma(2)(H)). We derive the spin distribution of primordial black holes and find that most of the primordial black holes are rapidly rotating near the extreme value a(*) = 1, where a(*) is the nondimensional Kerr parameter at their formation. The smaller sigma(H) is, the stronger the tendency towards the extreme rotation. Combining this result with the effect of anisotropy, we numerically and semianalytically estimate the production rate beta(0) of primordial black holes. Then we find that beta(0) similar or equal to 1.9 x 10(-6) f(q)(q(c))I-6 sigma(2)(H) exp(-0.15I(4/3)sigma(-2/3)(H) for sigma(H) less than or similar to 0.005, while beta(0). 0.05556 sigma(5)(H) for 0.005 less than or similar to sigma(H) less than or similar to 0.2, where f(q)(q(c)) is the fraction of masses whose q is smaller than q(c) and we assume f(q)(q(c)) is not too small. We argue that matter domination significantly enhances the production of primordial black holes despite the suppression factor. If the end time t(end) of the matter-dominated phase satisfies t(end) less than or similar to (0.4I sigma(H))(-1)t(H), the effect of the finite duration significantly suppresses primordial black hole formation and weakens the tendency towards large spins.

DOI： 10.1103/PhysRevD.96.083517

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We consider a head-on collision of two massive particles that move in the equatorial plane of an extremal Kerr black hole, which results in the production of two massless particles. Focusing on a typical case, where both of the colliding particles have zero angular momenta, we show that a massless particle produced in such a collision can escape to infinity with arbitrarily large energy in the near-horizon limit of the collision point. Furthermore, if we assume that the emission of the produced massless particles is isotropic in the center-of-mass frame but confined to the equatorial plane, the escape probability of the produced massless particle approaches 5/12, and almost all escaping massless particles have arbitrarily large energy at infinity and an impact parameter approaching 2GM/c(2), where M is the mass of the black hole.

DOI： 10.1103/PhysRevD.95.124019

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Institute of Physics Publishing  

We simulate the spindle gravitational collapse of a collisionless particle system in a 3D numerical relativity code and compare the qualitative results with the old work done by Shapiro and Teukolsky (ST) (1991 Phys. Rev. Lett. 66 994). The simulation starts from the prolate-shaped distribution of particles and a spindle collapse is observed. The peak value and its spatial position of curvature invariants are monitored during the time evolution. We find that the peak value of the Kretschmann invariant takes a maximum at some moment, when there is no apparent horizon, and its value is greater for a finer resolution, which is consistent with what is reported in ST. We also find a similar tendency for the Weyl curvature invariant. Therefore, our results lend support to the formation of a naked singularity as a result of the axially symmetric spindle collapse of a collisionless particle system in the limit of infinite resolution. However, unlike in ST, our code does not break down then but goes well beyond. We find that the peak values of the curvature invariants start to gradually decrease with time for a certain period of time. Another notable difference from ST is that, in our case, the peak position of the Kretschmann curvature invariant is always inside the matter distribution.

DOI： 10.1088/1361-6382/aa6ad5

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Gravitational lensing is a good probe into the topological structure of dark gravitating celestial objects. In this paper, we investigate the light curve of a light ray that passes through the throat of an Ellis wormhole, the simplest example of traversable wormholes. The method developed here is also applicable to other traversable wormholes. To study whether the light curve of a light ray that passes through a wormhole throat is distinguishable from that which does not, we also calculate light curves without the passage of a throat for an Ellis wormhole, a Schwarzschild black hole, and an ultrastatic wormhole with the spatial geometry identical to that of the Schwarzschild black hole in the following two cases: (i) "microlensing," where the source, lens, and observer are almost aligned in this order and the light ray starts at the source, refracts in the weak gravitational field of the lens with a small deflection angle, and reaches the observer; and (ii) "retrolensing," where the source, observer, and lens are almost aligned in this order, and the light ray starts at the source, refracts in the vicinity of the light sphere of the lens with a deflection angle very close to pi, and reaches the observer. We find that the light curve of the light ray that passes through the throat of the Ellis wormhole is clearly distinguishable from that by the microlensing but not from that by the retrolensing. This is because the light curve of a light ray that passes by a light sphere of a lens with a large deflection angle has common characters, irrespective of the details of the lens object. This implies that the light curves of the light rays that pass through the throat of more general traversable wormholes are qualitatively the same as that of the Ellis wormhole.

DOI： 10.1103/PhysRevD.95.024030

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

We investigate primordial black hole formation in the matter-dominated phase of the universe, where nonspherical effects in gravitational collapse play a crucial role. This is in contrast to the black hole formation in a radiation-dominated era. We apply the Zel'dovich approximation, Thorne's hoop conjecture, and Doroshkevich's probability distribution and subsequently derive the production probability beta(0) of primordial black holes. The numerical result obtained is applicable even if the density fluctuation sigma at horizon entry is of the order of unity. For sigma &lt;&lt; 1, we find a semi-analytic formula beta(0) similar or equal to 0.05556 sigma(5), which is comparable to the Khlopov-Polnarev formula. We find that the production probability in the matter-dominated era is much larger than that in the radiation-dominated era for sigma greater than or similar to 0.05, while they are comparable with each other for sigma greater than or similar to 0.05. We also discuss how s can be written in terms of primordial curvature perturbations.

DOI： 10.3847/1538-4357/833/1/61

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We study the self-similar motion of a string in a self-similar spacetime by introducing the concept of a self-similar string, which is defined as the world sheet to which a homothetic vector field is tangent. It is shown that in Nambu-Goto theory, the equations of motion for a self-similar string reduce to those for a particle. Moreover, under certain conditions such as the hypersurface orthogonality of the homothetic vector field, the equations of motion for a self-similar string simplify to the geodesic equations on a (pseudo)Riemannian space. As a concrete example, we investigate a self-similar Nambu-Goto string in a spatially flat Friedmann-Lemutre-Robertson-Walker expanding universe with self-similarity and obtain solutions of open and closed strings, which have various nontrivial configurations depending on the rate of the cosmic expansion. For instance, we obtain a circular solution that evolves linearly in the cosmic time while keeping its configuration by the balance between the effects of the cosmic expansion and string tension. We also show the instability for linear radial perturbation of the circular solutions.

DOI： 10.1103/PhysRevD.94.064029

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：OXFORD UNIV PRESS INC  

We construct spacetimes which provide spherical and nonspherical models of black hole formation in the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) universe with the Lemaitre-Tolman-Bondi solution and the Szekeres quasispherical solution, respectively. These dust solutions may contain both shell-crossing and shell-focusing naked singularities. These singularities can be physically regarded as the breakdown of dust description, where strong pressure gradient force plays a role. We adopt the simultaneous big bang condition to extract a growing mode of adiabatic perturbation in the flat FLRW universe. If the density perturbation has a sufficiently homogeneous central region and a sufficiently sharp transition to the background FLRW universe, its central shell-focusing singularity is globally covered. If the density concentration is sufficiently large, no shell-crossing singularity appears and a black hole is formed. If the density concentration is not sufficiently large, a shell-crossing singularity appears. In this case, a large dipole moment significantly advances shell-crossing singularities and they tend to appear before the black hole formation. In contrast, a shell-crossing singularity unavoidably appears in the spherical and nonspherical evolution of cosmological voids. The present analysis is general and applicable to cosmological nonlinear structure formation described by these dust solutions.

DOI： 10.1093/ptep/ptw123

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

In the accretion flow of a fluid, its velocity may transit from subsonic to supersonic. The point at which such a transition occurs is called the sonic point and is often mathematically special. We consider the steady-state and spherically symmetric accretion problem of an ideal photon gas in general static spherically symmetric spacetimes, neglecting backreaction. Our main result is that the equation of state (EOS) of an ideal photon gas leads to a correspondence between its sonic point and the photon sphere of the spacetime in general situations. Moreover, we also show that in spite of the dependence of the EOS on the dimension of spacetime, this correspondence holds for spacetimes of arbitrary dimensions.

DOI： 10.1103/PhysRevD.94.044053

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We propose a consistent analytic approach to the efficiency of collisional Penrose process in the vicinity of a maximally rotating Kerr black hole. We focus on a collision with arbitrarily high center-of-mass energy, which occurs if either of the colliding particles has its angular momentum fine-tuned to the critical value to enter the horizon. We show that if the fine-tuned particle is ingoing on the collision, the upper limit of the efficiency is (2 + root 3) (2 - root 2) similar or equal to 2.186, while if the fine-tuned particle is bounced back before the collision, the upper limit is (2 + root 3)(2) similar or equal to 13.93. Despite earlier claims, the former can be attained for inverse Compton scattering if the fine-tuned particle is massive and starts at rest at infinity, while the latter can be attained for various particle reactions, such as inverse Compton scattering and pair annihilation, if the fine-tuned particle is either massless or highly relativistic at infinity. We discuss the difference between the present and earlier analyses.

DOI： 10.1103/PhysRevD.94.024038

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Vacuum excitation by time-varying boundary conditions is not only of fundamental importance but also has recently been confirmed in a laboratory experiment. In this paper, we study the vacuum excitation of a scalar field by the instantaneous appearance and disappearance of a two-sided Dirichlet wall in the middle of a one-dimensional cavity, as toy models of bifurcating and merging spacetimes, respectively. It is shown that the energy flux emitted positively diverges on the null lines emanating from the appearance and disappearance events, which is analogous to the result of Anderson and DeWitt. This result suggests that the semiclassical effect prevents the spacetime both from bifurcating and merging. In addition, we argue that the diverging flux in the disappearance case plays an interesting role to compensate for the low ambient energy density after the disappearance, which is lower than the zero-point level.

DOI： 10.1103/PhysRevD.94.025006

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

The origin of the ultrahigh-energy particles we receive on Earth from outer space such as EeV cosmic rays and PeV neutrinos remains an enigma. All mechanisms known to us currently make use of electromagnetic interaction to accelerate charged particles. In this paper, we propose a mechanism exclusively based on gravity rather than electromagnetic interaction. We show that it is possible to generate ultrahigh-energy particles starting from particles with moderate energies using the collisional Penrose process in an overspinning Kerr spacetime transcending the Kerr bound only by an infinitesimal amount, i.e., with the Kerr parameter a = M(1 + epsilon), where we take the limit epsilon -&gt; 0(+.) We consider two massive particles starting from rest at infinity that collide at r = M with divergent center-of-mass energy and produce two massless particles. We show that massless particles produced in the collision can escape to infinity with the ultrahigh energies exploiting the collisional Penrose process with the divergent efficiency eta similar to 1/root epsilon -&gt; infinity. Assuming the isotropic emission of massless particles in the center-of-mass frame of the colliding particles, we show that half of the particles created in the collisions escape to infinity with the divergent energies, while the proportion of particles that reach infinity with finite energy is minuscule. To a distant observer, ultrahigh-energy particles appear to originate from a bright spot which is at the angular location xi similar to 2M / r(obs) with respect to the singularity on the side which is rotating toward the observer. We compute the spectrum of the high-energy massless particles and show that anisotropy in the emission in the center-of-mass frame leaves a distinct signature on its shape. Since the anisotropy is dictated by the differential cross section of the underlying particle physics process, the observation of the spectrum can constrain the particle physics model and serve as a unique probe into fundamental physics at ultrahigh energies at which particles collide. Thus, the existence of the near-extremal overspinning Kerr geometry in the Universe, either as a transient or permanent configuration, would have deep implications on astrophysics as well as fundamental particle physics.

DOI： 10.1103/PhysRevD.93.104015

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

The center-of-mass energy of two particles can become arbitrarily large if they collide near the event horizon of an extremal Kerr black hole, which is called the Banados-Silk-West effect. We consider such a high-energy collision of two particles which started from infinity and follow geodesics in the equatorial plane and investigate the energy extraction from such a high-energy particle collision and the production of particles in the equatorial plane. We analytically show that, on the one hand, if the produced particles are as massive as the colliding particles, the energy-extraction efficiency is bounded by 2.19 approximately. On the other hand, if a very massive particle is produced as a result of the high-energy collision, which has negative energy and necessarily falls into the black hole, the upper limit of the energy-extraction efficiency is increased to (2 + root 3)(2) similar or equal to 13.9. Thus, higher efficiency of the energy extraction, which is typically as large as 10, provides strong evidence for the production of a heavy particle.

DOI： 10.1103/PhysRevD.93.044054

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Institute of Physics Publishing  

The effect of the Gauss-Bonnet term on the existence and dynamical stability of thin-shell wormholes as negative tension branes is studied in the arbitrary-dimensional spherically, planar and hyperbolically symmetric spacetimes. We consider radial perturbations against the shell for the solutions that have the Z2 symmetry and admit the general relativistic limit. It is shown that the Gauss-Bonnet term shrinks the parameter region that admits static wormholes. The effect of the Gauss-Bonnet term on the stability depends on the spacetime symmetry. For planar symmetric wormholes, the Gauss-Bonnet term does not affect their stability. If the coupling constant is positive but small, the Gauss-Bonnet term tends to destabilize spherically symmetric wormholes, while it stabilizes hyperbolically symmetric wormholes. The Gauss-Bonnet term can destabilize hyperbolically symmetric wormholes as a non-perturbative effect, but spherically symmetric wormholes cannot be stable.

DOI： 10.1088/0264-9381/32/23/235021

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Language：English   Publishing type：Research paper (scientific journal)  

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：EPL ASSOCIATION, EUROPEAN PHYSICAL SOCIETY  

We make a critical comparison between ultra-high-energy particle collisions around an extremal Kerr black hole and that around an over-spinning Kerr singularity, mainly focusing on the issue of the timescale of collisions. We show that the time required for two massive particles with the proton mass or two massless particles of GeV energies to collide around the Kerr black hole with Planck energy is several orders of magnitude longer than the age of the Universe for astro-physically relevant masses of black holes, whereas time required in the over-spinning case is of the order of ten million years, which is much shorter than the age of the Universe. Thus, from the point of view of observation of Planck scale collisions, the over-spinning Kerr geometry, subject to their occurrence, has distinct advantage over their black-hole counterparts. Copyright (C) EPLA, 2015

DOI： 10.1209/0295-5075/110/30004

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We construct cosmological long-wavelength solutions without symmetry in general gauge conditions which are compatible with the long-wavelength scheme. We then specify the relationship among the solutions in different time slicings. Nonspherical long-wavelength solutions are particularly important for primordial structure formation in the epoch of very soft equations of state. Applying this general framework to spherical symmetry, we show the equivalence between long-wavelength solutions in the constant mean curvature slicing with conformally flat spatial coordinates and asymptotic quasihomogeneous solutions in the comoving slicing with the comoving threading. We derive the correspondence relation between these two solutions and compare the results of numerical simulations of primordial black hole (PBH) formation in these two different approaches. To discuss the PBH formation, it is convenient and conventional to use (delta) over tilde (c), the value which the averaged density perturbation at threshold in the comoving slicing would take at horizon entry in the lowest-order long-wavelength expansion. We numerically find that within (approximately) compensated models, the sharper the transition from the overdense region to the Friedmann-Robertson-Walker universe is, the larger the (delta) over tilde (c) becomes. We suggest that, for the equation of state p = (Gamma-1)rho, we can apply the analytic formulas for the minimum (delta) over tilde (c,min) similar or equal to [3 Gamma/(3 Gamma + 2)]sin(2)[pi root Gamma - 1/(3 Gamma - 2)] and the maximum (delta) over tilde (c,max) similar or equal to 3 Gamma/(3 Gamma + 2). As for the threshold peak value of the curvature variable psi(0,c), we find that the sharper the transition is, the smaller the psi(0,c) becomes. We analytically explain this intriguing feature qualitatively with a compensated top-hat density model. Using simplified models, we also analytically deduce an environmental effect that psi(0,c) can be significantly larger (smaller) if the underlying perturbation of much longer wavelength is positive (negative).

DOI： 10.1103/PhysRevD.91.084057

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

The claim that an overdense (positive-curvature) region in the early Universe cannot extend beyond some maximum scale and remain part of our Universe, first made 40 years ago, has recently been questioned by Kopp et al. Their analysis is elucidating and demonstrates that one cannot constrain the form of primordial density perturbations using this argument. However, the notion of a separate universe scale still applies and there is also an upper limit on the scale of a region collapsing to a black hole at any epoch, these scales being simply related. We calculate these scales for equations of state of the form p = k rho c(2) with -1 &lt; k &lt; infinity, refining earlier calculations on account of the Kopp et al. criticisms. For -1/3 &lt; k &lt; infinity, the scale is always of the order of the cosmological particle horizon size, with a numerical factor depending on k. This confirms the earlier claim that a primordial black hole cannot be much larger than the particle horizon at formation. For -1 &lt; k &lt; -1/3, as expected for some periods in the history of the Universe, the situation changes radically, in that a sufficiently large positive-curvature region produces a baby universe rather than a black hole. There is still a separate universe scale but the interpretation of these solutions requires care.

DOI： 10.1103/PhysRevD.91.084048

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：World Scientific  

Bañados, Silk and West1 have indicated that Kerr black holes act as particle accelerators to arbitrarily high energy. In this context, we discuss the relevance of an ISCO particle around a nearly maximally rotating black hole. This implies that high-velocity collisions of compact objects are naturally expected around a rapidly rotating supermassive black hole. We also discuss that the particle acceleration would not be so sensitive to gravitational radiation reaction if the mass ratio of the inspiraling particle to the black hole is sufficiently small.

DOI： 10.1142/9789814623995_0181

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：World Scientific  

We present an expression for the center-of-mass (CM) energy of two colliding general geodesic massive and massless particles around a Kerr black hole. We show that the CM energy can be arbitrarily high only in the limit to the horizon and then derive a formula for the CM energy of two general geodesic particles colliding near the horizon. To have an arbitrarily high CM energy, the angular momentum of either of the two particles must be fine-tuned to the critical value. We show that, in the direct collision scenario, the collision with an arbitrarily high CM energy can occur near the horizon of maximally rotating black holes not only at the equator but also on a belt centered at the equator. This belt lies between latitudes ±acos(√ 3 − 1) ≃ ±42.94°.

DOI： 10.1142/9789814623995_0183

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：World Scientific  

Horava-Lifshitz gravity has covariance only under the foliation-preserving diffeomorphism. This implies that the quantities on the constant-time hypersurfaces should be regular. In the original theory, the projectability condition which strongly restricts the lapse function is proposed. We assume that a star is filled with a perfect fluid, that it has the reflection symmetry about the equatorial plane. As a result, we find a no-go theorem for stationary axisymmetric star solutions in projectable Horava-Lifshitz gravity under the physically reasonable assumptions on the matter sector.

DOI： 10.1142/9789814623995_0099

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

The angular momentum of the Kerr singularity should not be larger than a threshold value so that it is enclosed by an event horizon: The Kerr singularity with the angular momentum exceeding the threshold value is naked. This fact suggests that if the cosmic censorship exists in our Universe, an over-spinning body without releasing its angular momentum cannot collapse to spacetime singularities. A simple kinematical estimate of two particles approaching each other supports this expectation and suggests the existence of a minimum size of an over-spinning body. But this does not imply that the geometry near the naked singularity cannot appear. By analyzing initial data, i.e., a snapshot of a spinning body, we see that an over-spinning body may produce a geometry close to the Kerr naked singularity around itself at least as a transient configuration.

DOI： 10.1103/PhysRevD.90.124079

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Primordial black holes (PBHs) are an important tool in cosmology to probe the<br />
primordial spectrum of small-scale curvature perturbations that reenter the<br />
cosmological horizon during radiation domination epoch. We numerically solve<br />
the evolution of spherically symmetric highly perturbed configurations to<br />
clarify the criteria of PBHs formation using a wide class of curvature profiles<br />
characterized by five parameters. It is shown that formation or non-formation<br />
of PBHs is determined essentialy by only two master parameters.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We study high energy particle collisions around higher dimensional black holes. It is shown that the center of mass energy can be arbitrarily large in the vicinity of the event horizon like the Banados, Silk and West (BSW) process in four dimensions if the following two conditions are satisfied: (i) the horizon is extremal and (ii) the parameters of either of the two colliding particles are fine-tuned, which is called a critical particle condition. We also show that a test particle which satisfies the critical particle condition can reach the event horizon from a distant region for a simple case. Finally, we discuss the relation between the BSW process and the linear instability of test fields around extremal black holes, the latter of which has been recently found by Aretakis [Commun. Math. Phys. 307, 17 (2011); Ann. Inst. Henri Poincare 12, 1491 (2011); J. Funct. Anal. 263, 2770 (2012); arXiv: 1206.6598; Classical Quantum Gravity 30, 095010 (2013); Phys. Rev. D 87, 084052 (2013)].

DOI： 10.1103/PhysRevD.89.024020

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

Primordial black holes (PBHs) are an important tool in cosmology to probe the primordial spectrum of small-scale curvature perturbations that reenter the cosmological horizon during radiation domination epoch. We numerically solve the evolution of spherically symmetric highly perturbed configurations to clarify the criteria of PBHs formation using an extremely wide class of curvature profiles characterized by five parameters, (in contrast to only two parameters used in all previous papers) which specify the curvature profiles not only at the central region but also at the outer boundary of configurations. It is shown that formation or non-formation of PBHs is determined essentialy by only two roaster parameters one of which can be presented as an integral of curvature over initial configurations and the other is presented in terms of the position of the boundary and the edge of the core.

DOI： 10.1088/1475-7516/2014/01/037

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Based on a physical argument, we derive a new analytic formula for the amplitude of density perturbation at the threshold of primordial black hole formation in the Universe dominated by a perfect fluid with the equation of state p = w rho c(2) for w &gt;= 0. The formula gives delta(UH)(Hc) = sin(2)[pi root w/(1 + 3w)] and (delta) over tilde (c) = [3(1 + w)/(5 + 3w)]sin(2)[pi root w/(1 + 3w)], where delta(UH)(Hc) and (delta) over tilde (c) are the amplitude of the density perturbation at the horizon crossing time in the uniform Hubble slice and the amplitude measure used in numerical simulations, respectively, while the conventional one gives delta(UH)(Hc) = w and (delta) over tilde (c) = 3w(1 + w)/(5 + 3w). Our formula shows a much better agreement with the result of recent numerical simulations both qualitatively and quantitatively than the conventional formula. For a radiation fluid, our formula gives delta(UH)(Hc) = sin(2)(root 3 pi/6) similar or equal to 0.6203 and (delta) over tilde (c) = (2/3)sin(2)(root 3 pi/6) similar or equal to 0.4135. We also discuss the maximum amplitude and the cosmological implications of the present result.

DOI： 10.1103/PhysRevD.88.084051

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

For particle collision near rapidly rotating Kerr black holes, the center-of-mass energy can be arbitrarily high if the angular momentum of either of the colliding particles is fine-tuned. Recently, it has been shown that particles which are produced by such a particle collision and escape to infinity cannot be very massive nor very energetic. For electrically charged black holes there is a similar phenomenon, where the center-of-mass energy for the collision of charged particles near the horizon can be arbitrarily high. One might expect that there would exist a similar bound on the energy and mass of particles that are produced by such a particle collision and escape to infinity. In this paper, however, we see that this expectation is not the case. We explicitly show that superheavy and highly energetic charged particles produced by the collision near maximally charged black holes can escape to infinity at least within classical theory if the backreaction and self-force of the particle can be neglected.

DOI： 10.1103/PhysRevD.87.127502

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：OXFORD UNIV PRESS INC  

The possible violation of the weak cosmic censorship hypothesis in astrophysical phenomena can provide us with information about trans-Planckian physics through observations. We present negative evidence, however, that one should not expect such a possibility at least when the deviation from spherical symmetry is negligible and the parameter values of collapse are astrophysically reasonable. Taking the Lema tre-Tolman-Bondi solution as the model most likely to counter the weak hypothesis, we show that the mass (greater than or similar to 1.5 M-circle dot) and density (greater than or similar to 1.5 x 10(15) g/cm(3)) of the collapsing object produce a gravitational field strong enough to capture any null rays soon after emanating from the singularity.

DOI： 10.1093/ptep/ptt027

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We propose the use of modulated spectra of astronomical sources due to gravitational lensing to probe Ellis wormholes. The modulation factor due to gravitational lensing by the Ellis wormhole is calculated. Within the geometrical optics approximation, the normal point-mass lens and the Ellis wormhole are indistinguishable unless we know the source's unlensed luminosity. This degeneracy is resolved with the significant wave effect in the low-frequency domain if we take the deviation from the geometrical optics into account. We can roughly estimate the upper bound for the number density of Ellis wormholes as nâ‰4×10-10AU-3 with throat radius a∼1 cm from the existing femtolensing analysis for compact objects. © 2013 American Physical Society.

DOI： 10.1103/PhysRevD.87.084045

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We propose the use of modulated spectra of astronomical sources due to gravitational lensing to probe Ellis wormholes. The modulation factor due to gravitational lensing by the Ellis wormhole is calculated. Within the geometrical optics approximation, the normal point-mass lens and the Ellis wormhole are indistinguishable unless we know the source's unlensed luminosity. This degeneracy is resolved with the significant wave effect in the low-frequency domain if we take the deviation from the geometrical optics into account. We can roughly estimate the upper bound for the number density of Ellis wormholes as n less than or similar to 4 X 10(-10)AU(-3) with throat radius a similar to 1 cm from the existing femtolensing analysis for compact objects. DOI: 10.1103/PhysRevD.87.084045

DOI： 10.1103/PhysRevD.87.084045

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We present a renormalization group analysis to Einstein-Rosen waves or vacuum spacetimes with whole-cylinder symmetry. It is found that self-similar solutions appear as fixed points in the renormalization group transformation. These solutions correspond to the explosive gravitational waves and the collapsing gravitational waves at late times and early times, respectively. Based on the linear perturbation analysis of the self-similar solutions, we conclude that the self-similar evolution is stable as explosive gravitational waves under the condition of no incoming waves, while it is weakly unstable as collapsing gravitational waves. The result implies that self-similar solutions can describe the asymptotic behavior of more general solutions for exploding gravitational waves and thus extends the similarity hypothesis in general relativity from spherical symmetry to cylindrical symmetry. © 2013 American Physical Society.

DOI： 10.1103/PhysRevD.87.064043

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It is well known that the sum of signed magnifications is invariant for mass lens systems. In this paper, we discuss the signed magnification sums of general spherical lens models, including the singular isothermal sphere, the Schwarzschild lens, and the Ellis wormhole, the last of which is an example of the traversable wormholes of the Morris-Thorne class. We show that the signed magnification sums are a very useful tool to distinguish exotic lens objects. For example, we show that one can distinguish the Ellis wormholes from the Schwarzschild lens with the signed magnification sums. © 2013 American Physical Society.

DOI： 10.1103/PhysRevD.87.024024

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

It is well known that the sum of signed magnifications is invariant for mass lens systems. In this paper, we discuss the signed magnification sums of general spherical lens models, including the singular isothermal sphere, the Schwarzschild lens, and the Ellis wormhole, the last of which is an example of the traversable wormholes of the Morris-Thorne class. We show that the signed magnification sums are a very useful tool to distinguish exotic lens objects. For example, we show that one can distinguish the Ellis wormholes from the Schwarzschild lens with the signed magnification sums. DOI: 10.1103/PhysRevD.87.024024

DOI： 10.1103/PhysRevD.87.024024

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For the past decade, gravitational lensing in the strong gravitational field has been studied eagerly. It is well known that, for the lensing by a black hole, an infinite number of Einstein rings are formed by the light rays which wind around the black hole nearly on the photon sphere, which are called relativistic Einstein rings. This is also the case for the lensing by a wormhole. In this paper, we study the Einstein ring and relativistic Einstein rings for the Schwarzschild black hole and the Ellis wormhole, the latter of which is an example of traversable wormholes of the Morris-Thorne class. Given the configuration of the gravitational lensing and the radii of the Einstein ring and relativistic Einstein rings, we can distinguish between a black hole and a wormhole in principle. We conclude that we can detect the relativistic Einstein rings by wormholes which have the radii of the throat a0.5pc at a Galactic center with the distance 10Mpc and which have a10AU in our Galaxy using the most powerful modern instruments which have the resolution of 10 -2arcsecond such as a 10-meter optical-infrared telescope. The black holes which make the Einstein rings of the same size as the ones by the wormholes are galactic supermassive black holes and the relativistic Einstein rings by the black holes are too small to measure with the current technology. We may test the hypotheses of astrophysical wormholes by using the Einstein ring and relativistic Einstein rings in the future. © 2012 American Physical Society.

DOI： 10.1103/PhysRevD.86.104062

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

For the past decade, gravitational lensing in the strong gravitational field has been studied eagerly. It is well known that, for the lensing by a black hole, an infinite number of Einstein rings are formed by the light rays which wind around the black hole nearly on the photon sphere, which are called relativistic Einstein rings. This is also the case for the lensing by a wormhole. In this paper, we study the Einstein ring and relativistic Einstein rings for the Schwarzschild black hole and the Ellis wormhole, the latter of which is an example of traversable wormholes of the Morris-Thorne class. Given the configuration of the gravitational lensing and the radii of the Einstein ring and relativistic Einstein rings, we can distinguish between a black hole and a wormhole in principle. We conclude that we can detect the relativistic Einstein rings by wormholes which have the radii of the throat a similar or equal to 0.5 pc at a Galactic center with the distance 10 Mpc and which have a similar or equal to 10 AU in our Galaxy using the most powerful modern instruments which have the resolution of 10(-2) arcsecond such as a 10-meter optical-infrared telescope. The black holes which make the Einstein rings of the same size as the ones by the wormholes are galactic supermassive black holes and the relativistic Einstein rings by the black holes are too small to measure with the current technology. We may test the hypotheses of astrophysical wormholes by using the Einstein ring and relativistic Einstein rings in the future.

DOI： 10.1103/PhysRevD.86.104062

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

The center-of-mass energy of two particles colliding near the horizon of a maximally rotating black hole can be arbitrarily high if the angular momentum of either of the incident particles is fine-tuned, which we call a critical particle. We study particle emission from such high-energy collision and reaction in the equatorial plane fully analytically. We show that the unconditional upper limit of the energy of the emitted particle is given by 218.6% of that of the injected critical particle, irrespective of the details of the reaction and this upper limit can be realized for massless particle emission. The upper limit of the energy extraction efficiency for this emission as a collisional Penrose process is given by 146.6%, which can be realized in the collision of two massive particles with optimized mass ratio. Moreover, we analyze perfectly elastic collision, Compton scattering, and pair annihilation and show that net positive energy extraction is really possible for these three reactions. The Compton scattering is most efficient among them and the efficiency can reach 134.3%. On the other hand, our result is qualitatively consistent with the earlier claim that the mass and energy of the emitted particle are at most of order the total energy of the injected particles and hence we can observe neither super-heavy nor super-energetic particles. The present paper places the baseline for the study of particle emission from high-energy collision near a rapidly rotating black hole.

DOI： 10.1103/PhysRevD.86.024027

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We study high energy charged particle collisions near the horizon in an electromagnetic field around a rotating black hole and reveal the condition of the fine-tuning to obtain arbitrarily large center-of-mass (CM) energy. We demonstrate that the CM energy can be arbitrarily large as the uniformly magnetized rotating black hole arbitrarily approaches maximal rotation under the situation that a charged particle plunges from the innermost stable circular orbit (ISCO) and collides with another particle near the horizon. Recently, Frolov [Phys. Rev. D 85, 024020 (2012)] proposed that the CM energy can be arbitrarily high if the magnetic field is arbitrarily strong, when a particle collides with a charged particle orbiting the ISCO with finite energy near the horizon of a uniformly magnetized Schwarzschild black hole. We show that the charged particle orbiting the ISCO around a spinning black hole needs arbitrarily high energy in the strong field limit. This suggests that Frolov's process is unstable against the black hole spin. Nevertheless, we see that magnetic fields may substantially promote the capability of rotating black holes as particle accelerators in astrophysical situations.

DOI： 10.1103/PhysRevD.85.104028

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

An inspiraling object of mass mu around a Kerr black hole of mass M(&gt;&gt; mu) experiences a continuous transition near the innermost stable circular orbit from adiabatic inspiral to plunge into the horizon as gravitational radiation extracts its energy and angular momentum. We investigate the collision of such an object with a generic counterpart around a Kerr black hole. We find that the angular momentum of the object is fine-tuned through gravitational radiation and that the high-velocity collision of the object with a generic counterpart naturally occurs around a nearly maximally rotating black hole. We also find that the center-of-mass energy can be far beyond the Planck energy for dark matter particles colliding around a stellar mass black hole and as high as 10(58) erg for stellar mass compact objects colliding around a supermassive black hole, where the present transition formalism is well justified. Therefore, rapidly rotating black holes can accelerate objects inspiraling around them to energy high enough to be of great physical interest.

DOI： 10.1103/PhysRevD.84.124032

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

In loop quantum cosmology, the Hamiltonian reduces to a finite difference operator and quantum dynamics are controlled by the difference equation. In this framework, Bojowald [M. Bojowald, Phys. Rev. Lett. 86, 5227 (2001).] showed that the initial singularity is absent in the twofold sense: (i) the spectrum of the inverse scale factor operator is bounded from above; (ii) the wave function of the Universe can be uniquely extended beyond the point which was the initial singularity in classical theory. In this paper, we study the initial singularity in this sense and the large-volume limit against the ambiguities in the discretization and the operator ordering within a homogeneous, isotropic and spatially flat model with the cosmological constant. We find that the absence of the singularity strongly depends on the choice of the operator ordering and the requirement for the absence singles out a very small class of orderings. Moreover we find a general ordering rule required for the absence of the singularity. We also find that the large-volume limit naturally recovers a smooth wave function in the discretization where each step corresponds to a fixed volume increment but not in the one where each step corresponds to a fixed area increment. If loop quantum cosmology is to be a phenomenological realization of full loop quantum gravity, these results are important to fix the theoretical ambiguities.

DOI： 10.1103/PhysRevD.83.104049

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DOI： 10.1088/0264-9381/28/9/094011

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We obtain an explicit expression for the center-of-mass (CM) energy of two colliding general geodesic massive and massless particles at any spacetime point around a Kerr black hole. Applying this, we show that the CM energy can be arbitrarily high only in the limit to the horizon and then derive a formula for the CM energy of two general geodesic particles colliding near the horizon in terms of the conserved quantities of each particle and the polar angle. We present the necessary and sufficient condition for the CM energy to be arbitrarily high in terms of the conserved quantities of each particle. To have an arbitrarily high CM energy, the angular momentum of either of the two particles must be fine-tuned to the critical value L-i = Omega(-1)(H) E-i, where Omega(H) is the angular velocity of the horizon and E-i and L-i are the energy and angular momentum of particle i(= 1, 2), respectively. We show that, in the direct collision scenario, the collision with an arbitrarily high CM energy can occur near the horizon of maximally rotating black holes not only at the equator but also on a belt centered at the equator. This belt lies between latitudes +/-acosd (root 3 - 1) similar or equal to +/-42.94 degrees. This is also true in the scenario through the collision of a last stable orbit particle.

DOI： 10.1103/PhysRevD.83.084041

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We derive a general formula for the center-of-mass (CM) energy for the near-horizon collision of two particles of the same rest mass on the equatorial plane around a Kerr black hole. We then apply this formula to a particle which plunges from the innermost stable circular orbit (ISCO) and collides with another particle near the horizon. It is found that the maximum value of the CM energy E(cm) is given by E(cm)/(2m(0)) similar or equal to 1.40/(4)root 1- a(*)(2) for a nearly maximally rotating black hole, where m(0) is the rest mass of each particle and a(*) is the nondimensional Kerr parameter. This coincides with the known upper bound for a particle which begins at rest at infinity within a factor of 2. Moreover, we also consider the collision of a particle orbiting the ISCO with another particle on the ISCO and find that the maximum CM energy is then given by E(cm)/(2m(0)) similar or equal to 1.77/(6)root 1 - a(*)(2). In view of the astrophysical significance of the ISCO, this result implies that particles can collide around a rotating black hole with an arbitrarily high CM energy without any artificial fine-tuning in an astrophysical context if we can take the maximal limit of the black hole spin or a(*) --&gt; 1. On the other hand, even if we take Thorne&apos;s bound on the spin parameter into account, highly or moderately relativistic collisions are expected to occur quite naturally, for E(cm)/(2m(0)) takes 6.95 (maximum) and 3.86 (generic) near the horizon and 4.11 (maximum) and 2.43 (generic) on the ISCO for a(*) = 0.998. This implies that high-velocity collisions of compact objects are naturally expected around a rapidly rotating supermassive black hole. Implications to accretion flows onto a rapidly rotating black hole are also discussed.

DOI： 10.1103/PhysRevD.83.024002

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：WORLD SCIENTIFIC PUBL CO PTE LTD  

We investigate static spherically symmetric vacuum solutions in the IR limit of projectable nonrelativistic quantum gravity, including the renormalizable quantum gravity recently proposed by Horava. It is found that the projectability condition plays an important role. Without the cosmological constant, the spacetime is uniquely given by the Schwarzschild solution. With the cosmological constant, the spacetime is uniquely given by the Kottler (Schwarzschild-(anti) de Sitter) solution for the entirely vacuum spacetime. However, in addition to the Kottler solution, the static spherical and hyperbolic universes are uniquely admissible for the locally empty region, for positive and negative cosmological constants, respectively, if its nonvanishing contribution to the global Hamiltonian constraint can be compensated by the nonempty or nonstatic region. This implies that static spherically symmetric entirely vacuum solutions would not admit the freedom to reproduce the observed flat rotation curves of galaxies. On the other hand, the result for locally empty regions implies that the IR limit of nonrelativistic quantum gravity theories do not simply recover general relativity but include it.

DOI： 10.1142/S0218271811018652

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IOP PUBLISHING LTD  

The specific angular momentum of a Kerr black hole must not be larger than its mass in the geometrical units. The observational confirmation of this bound which we call a Kerr bound directly suggests the existence of a black hole. On the other hand, the violation of this bound may suggest the existence of a superspinning object which might be suggested from a string theory argument. In order to investigate observational testability of this bound by using the X-ray energy spectrum of black hole candidates, we calculate the energy spectra from an optically thick and geometrically thin accretion disk of a superspinning object which is described by a Kerr metric but whose specific angular momentum is larger than its mass, and then compare the spectra of this object with those of a black hole. Based on this calculation, we present that the observational confirmation of the Kerr bound is very hard but the violation of it may be detectable if only the continuum X-ray spectrum of the disk is available.

DOI： 10.1088/1742-6596/314/1/012084

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We investigate static spherically symmetric vacuum solutions in the IR limit of projectable nonrelativistic quantum gravity, including the renormalisable quantum gravity recently proposed by Horava, with an emphasis on the uniqueness of the solutions. It is found that the projectability condition plays an important role. Without the cosmological constant, the spacetime is uniquely given by the Schwarzschild solution. With the cosmological constant, the spacetime is uniquely given by the Kottler (Schwarzschild-(anti) de Sitter) solution for the entirely vacuum spacetime. However, in addition to the Kottler solution, the static spherical and hyperbolic universes are uniquely admissible for the locally empty region, for the positive and negative cosmological constants, respectively. This implies that static spherically symmetric entirely vacuum solutions would not admit the freedom to reproduce the observed flat rotation curves of galaxies.

DOI： 10.1088/1742-6596/314/1/012120

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

In this paper we continue our study on the accretion process onto superspinning Kerr objects with no event horizon (super-spinars). We discuss the counterpart of the Bondi accretion onto black holes. We first report the results of our numerical simulations. We found a quasi-steady-state configuration for any choice of the parameters of our model. The most interesting feature is the presence of hot outflows. Unlike jets and outflows produced around black holes, which are thought to be powered by magnetic fields and emitted from the poles, here the outflows are produced by the repulsive gravitational force at a small distance from the super-spinar and are ejected around the equatorial plane. In some circumstances, the amount of matter in the outflow is considerable, which can indeed significantly reduce the gas mass accretion rate. Finally, we discuss a possible scenario of the accretion process in more realistic situations, which cannot be simulated by our code.

DOI： 10.1103/PhysRevD.81.104004

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A space gravitational-wave antenna, DECIGO (DECI-hertz interferometer Gravitational wave Observatory), will provide fruitful insights into the universe, particularly on the formation mechanism of supermassive black holes, dark energy and the inflation of the universe. In the current pre-conceptual design, DECIGO will be comprising four interferometer units; each interferometer unit will be formed by three drag-free spacecraft with 1000 km separation. Since DECIGO will be an extremely challenging mission with high-precision formation flight with long baseline, it is important to increase the technical feasibility before its planned launch in 2027. Thus, we are planning to launch two milestone missions. DECIGO pathfinder (DPF) is the first milestone mission, and key components for DPF are being tested on ground and in orbit. In this paper, we review the conceptual design and current status of DECIGO and DPF.

DOI： 10.1088/0264-9381/27/8/084010

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The specific angular momentum of a Kerr black hole must not be larger than its mass. The observational confirmation of this bound which we call a Kerr bound directly suggests the existence of a black hole. In order to investigate observational testability of this bound by using the x-ray energy spectrum of black hole candidates, we calculate energy spectra for a super-spinning object (or a naked singularity) which is described by a Kerr metric but whose specific angular momentum is larger than its mass, and then compare the spectra of this object with those of a black hole. We assume an optically thick and geometrically thin disk around the super-spinning object and calculate its thermal energy spectrum seen by a distant observer by solving general relativistic radiative transfer equations including usual special and general relativistic effects, such as Doppler boosting, gravitational redshift, light bending and frame-dragging. Surprisingly, for a given black hole, we can always find its super-spinning counterpart with its spin a in the range whose observed spectrum is very similar to and practically indistinguishable from that of the black hole. As a result, we conclude that to confirm the Kerr bound we need more than the x-ray thermal spectrum of the black hole candidates. © 2010 IOP Publishing Ltd.

DOI： 10.1088/0264-9381/27/7/075003

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Language：English   Publishing type：Research paper (international conference proceedings)  

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

The accretion process onto spinning objects in Kerr spacetimes is studied with numerical simulations. Our results show that accretion onto compact objects with Kerr parameter (characterizing the spin) vertical bar a vertical bar &lt; M and vertical bar a vertical bar &gt; M is very different. In the superspinning case, for vertical bar a vertical bar moderately larger than M, the accretion onto the central object is extremely suppressed due to a repulsive force at short distance. The accreting matter cannot reach the central object, but instead is accumulated around it, forming a high density cloud that continues to grow. The radiation emitted in the accretion process will be harder and more intense than the one coming from standard black holes; e.g. gamma-rays could be produced as seen in some observations. Gravitational collapse of this cloud might even give rise to violent bursts. As vertical bar a vertical bar increases, a larger amount of accreting matter reaches the central object and the growth of the cloud becomes less efficient. Our simulations find that a quasisteady state of the accretion process exists for vertical bar a vertical bar/M greater than or similar to 1.4, independently of the mass accretion rate at large radii. For such high values of the Kerr parameter, the accreting matter forms a thin disk at very small radii. We provide some analytical arguments to strengthen the numerical results; in particular, we estimate the radius where the gravitational force changes from attractive to repulsive and the critical value vertical bar a vertical bar/M approximate to 1.4 separating the two qualitatively different regimes of accretion. We briefly discuss the observational signatures which could be used to look for such exotic objects in the Galaxy and/or in the Universe.

DOI： 10.1103/PhysRevD.80.104023

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Language：English   Publishing type：Research paper (other academic)  

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

In loop quantum cosmology there may be a superinflation phase in the very early universe, in which a single scalar field with a negative power-law potential V = -M(4)(phi/M)(beta) plays an important role. Since the effective horizon root SD/H controls the behavior of quantum fluctuation instead of the usual Hubble horizon, we assume the following inflation scenario: the superinflation starts when the quantum state of the scalar field emerges into the classical regime and ends when the effective horizon becomes the Hubble horizon, and the effective horizon scale never gets shorter than the Planck length. From consistency with the WMAP 5 yr data, we place a constraint on the parameters of the potential (beta and M) and the energy density at the end of the superinflation, depending on the volume correction parameter n.

DOI： 10.1103/PhysRevD.80.063538

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We numerically study the dynamics of an imploding hollow cylinder composed of dust. Since there is no cylindrical black hole in 4-dimensional spacetime with physically reasonable energy conditions, a collapsed dust cylinder involves a naked singularity accompanied by its causal future, or a fatal singularity that terminates the history of the whole universe. In a previous paper, the present authors have shown that if the dust is assumed to be composed of collisionless particles Such that these particles go through the symmetry axis of the cylinder, then the scalar polynomial singularity formed on the symmetry axis is so weak that almost all the geodesics are complete, and thus effectively no singularity forms by the collapse of a hollow dust cylinder. By contrast, in this paper, we assume that all the collapsed dust settles down on the symmetry axis by changing its equation of state. Obtained solutions are the straightforward extension of Morgan&apos;s null dust Solution, in which no gravitational radiation is emitted. However, in the present case with timelike dust, an infinite amount of C-energy initially stored in the system is released through gravitational radiation. We also show that the gravitational waves asymptotically behave in a self-similar manner.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

The self-similarity hypothesis claims that in classical general relativity, spherically symmetric solutions may naturally evolve to a self-similar form in certain circumstances. In this context, the validity of the corresponding hypothesis in nonspherical geometry is very interesting as there may exist gravitational waves. We investigate self-similar vacuum solutions to the Einstein equation in the so-called whole-cylinder symmetry. We find that those solutions are reduced to part of the Minkowski spacetime with a regular or conically singular axis and with trivial or nontrivial topology if the homothetic vector is orthogonal to the cylinders of symmetry. These solutions are analogous to the Milne universe, but only in the direction parallel to the axis. Using these solutions, we discuss the nonuniqueness (and nonvanishing nature) of C energy and the existence of a cylindrical trapping horizon in Minkowski spacetime. Then, as we generalize the analysis, we find a two-parameter family of self-similar vacuum solutions, where the homothetic vector is not orthogonal to the cylinders in general. The family includes the Minkowski, the Kasner, and the cylindrical Milne solutions. The obtained solutions describe the interior to the exploding (imploding) shell of gravitational waves or the collapse (explosion) of gravitational waves involving singularities from nonsingular initial data in general. Since recent numerical simulations strongly suggest that one of these solutions may describe the asymptotic behavior of gravitational waves from the collapse of a dust cylinder, this means that the self-similarity hypothesis is naturally generalized to cylindrical symmetry.

DOI： 10.1103/PhysRevD.80.024025

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

DECIGO pathfinder (DPF) is a milestone satellite mission for DECIGO (DECi-hertz Interferometer Gravitational wave Observatory), which is a future space gravitational wave antenna. DECIGO is expected to provide fruitful insights into the universe, particularly about dark energy, the formation mechanism of supermassive black holes and the inflation of the universe. Since DECIGO will be an extremely challenging mission, which will be formed by three drag-free spacecraft with 1000 km separation, it is important to increase the technical feasibility of DECIGO before its planned launch in 2024. Thus, we are planning to launch two milestone missions: DPF and pre-DECIGO. In this paper, we review the conceptual design and current status of the first milestone mission, DPF.

DOI： 10.1088/0264-9381/26/9/094019

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Motivated by the cosmological wormhole solutions obtained from our recent numerical investigations, we provide a definition of a wormhole which applies to dynamical situations. Our numerical solutions do not have timelike trapping horizons but they are wormholes in the sense that they connect two or more asymptotic regions. Although the null energy condition must be violated for static wormholes, we find that it can still be satisfied in the dynamical context. Two analytic solutions for a cosmological wormhole connecting two Friedmann universes without trapping horizons are presented.

DOI： 10.1103/PhysRevD.79.044034

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DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) is the planned Japanese space gravitational wave antenna, aiming to detect gravitational waves from astrophysically and cosmologically significant sources mainly between 0.1 Hz and 10 Hz and thus to open a new window for gravitational wave astronomy and for the universe. DECIGO will consist of three drag-free spacecraft, 1000 km apart from each other, whose relative displacements are measured by a differential Fabry-Perot interferometer. We plan to launch DECIGO in middle of 2020s, after sequence of two precursor satellite missions, DECIGO pathfinder and Pre-DECIGO, for technology demonstration required to realize DECIGO and hopefully for detection of gravitational waves from our galaxy or nearby galaxies. © 2009 IOP Publishing Ltd.

DOI： 10.1088/1742-6596/154/1/012040

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In this paper, we study the dynamics of a hollow spherical matter collapsing with a very large initial velocity. The spacetime is initially very similar to the Vaidya solution, and the deviations from this background are treated perturbatively. The equations of state for radial pressure pR = kρ and tangential one pT = wρ with constants k and w are assumed. We find for the case of equations of state k &lt
1 and 0 &lt
w ≤ 1 that the initial velocity, which is nearly the speed of light, is strongly decelerated. This result implies that the pressure is essential to the property of singularity formation in gravitational collapse even for initially nearly light-speed collapse. By contrast, in cases with the negative tangential pressure, the present result implies that the central naked singularity similar to that of the Vaidya spacetime can be formed, even though the radial pressure is positive, and the weak, strong and dominant energy conditions hold. Especially, in the case of w &lt
-(1 - k)/4, the high-speed collapse will produce the spacetime structure very similar to that of the Vaidya spacetime. © 2009 IOP Publishing Ltd.

DOI： 10.1088/0264-9381/26/3/035007

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：AMER INST PHYSICS  

Based on the studies on self-similar black holes in an expanding universe in 1970&apos;s, it has been generally accepted that such black holes are not possible. We see our recent analytical and numerical results that self-similar black holes are indeed possible in an accelerating universe with dark energy using a simplest model. We discuss the implication of this result in cosmology. Finally, we also see the possibility of self-similar black holes with quintessence, or scalar field with a flat potential.

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：MATH SOC JAPAN  

Einstein's field equations in general relativity admit a variety of solutions with spacetime singularities. Numerical relativity has recently revealed the properties of somewhat generic spacetime singularities. It has been found that in a variety of systems self-similar solutions can describe asymptotic or intermediate behaviour of more general solutions in an approach to singularities. The typical example is the convergence to an attractor self-similar solution in gravitational collapse. This is closely related to the cosmic censorship violation in the spherically symmetric collapse of a perfect fluid. The self-similar solution also plays an important role in critical phenomena in gravitational collapse. The critical phenomena are understood as the intermediate behaviour around a critical self-similar solution. We see that the convergence and critical phenomena are understood in a unified manner in terms of attractors of codimension zero and one, respectively, in renormalisation group flow.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Lemaitre-Tolman-Bondi models as specific spherically symmetric solutions of general relativity simplify in their reduced form some of the mathematical ingredients of black hole or cosmological applications. The conditions imposed in addition to spherical symmetry turn out to take a simple form at the kinematical level of loop quantum gravity, which allows a discussion of their implications at the quantum level. Moreover, the spherically symmetric setting of inhomogeneity illustrates several nontrivial properties of lattice refinements of discrete quantum gravity. Nevertheless, the situation at the dynamical level is quite nontrivial and thus provides insights to the anomaly problem. At an effective level, consistent versions of the dynamics are presented which implement the conditions together with the dynamical constraints of gravity in an anomaly-free manner. These are then used for analytical as well as numerical investigations of the fate of classical singularities, including nonspacelike ones, as they generically develop in these models. None of the corrections used here resolve those singularities by regular effective geometries. However, there are numerical indications that the collapse ends in a tamer shell-crossing singularity prior to the formation of central singularities for mass functions giving a regular conserved mass density. Moreover, we find quantum gravitational obstructions to the existence of exactly homogeneous solutions within this class of models. This indicates that homogeneous models must be seen in a wider context of inhomogeneous solutions and their reduction in order to provide reliable dynamical conclusions.

DOI： 10.1103/PhysRevD.78.064057

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We investigate self-similar solutions which are asymptotic to the Friedmann universe at spatial infinity and contain a scalar field with potential. The potential is required to be exponential by self-similarity. It is found that there are two distinct one-parameter families of asymptotic solutions, one is asymptotic to the proper Friedmann universe, while the other is asymptotic to the quasi-Friedmann universe, i.e., the Friedmann universe with anomalous solid angle. The asymptotically proper Friedmann solution is possible only if the universe is accelerated or the potential is negative. If the potential is positive, the density perturbation in the asymptotically proper Friedmann solution rapidly falls off at spatial infinity, while the mass perturbation is compensated. In the asymptotically quasi-Friedmann solution, the density perturbation falls off only in proportion to the inverse square of the areal radius and the relative mass perturbation approaches a nonzero constant at spatial infinity. The present result shows that a necessary condition holds in order that a self-gravitating body grows self-similarly due to the constant accretion of quintessence in an accelerating universe.

DOI： 10.1103/PhysRevD.77.124036

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Language：Japanese   Publishing type：Research paper (scientific journal)  

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We use a combination of numerical and analytical methods, exploiting the equations derived in a preceding paper, to classify all spherically symmetric self-similar solutions which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state p=(γ-1)μ with 0&lt
γ&lt
2/3. The expansion of the Friedmann universe is accelerated in this case. We find a one-parameter family of self-similar solutions representing a black hole embedded in a Friedmann background. This suggests that, in contrast to the positive pressure case, black holes in a universe with dark energy can grow as fast as the Hubble horizon if they are not too large. There are also self-similar solutions which contain a central naked singularity with negative mass and solutions which represent a Friedmann universe connected to either another Friedmann universe or some other cosmological model. The latter are interpreted as self-similar cosmological white hole or wormhole solutions. The throats of these wormholes are defined as two-dimensional spheres with minimal area on a spacelike hypersurface and they are all nontraversable because of the absence of a past null infinity. © 2008 The American Physical Society.

DOI： 10.1103/PhysRevD.77.024023

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state p=(gamma - 1)mu with 0 &lt; gamma &lt; 2/3. This corresponds to a "dark energy" fluid and the Friedmann solution is accelerated in this case due to antigravity. This extends the previous analysis of spherically symmetric self-similar solutions for fluids with positive pressure (gamma &gt; 1). However, in the latter case there is an additional parameter associated with the weak discontinuity at the sonic point and the solutions are only asymptotically "quasi-Friedmann," in the sense that they exhibit an angle deficit at large distances. In the 0 &lt; gamma &lt; 2/3 case, there is no sonic point and there exists a one-parameter family of solutions which are genuinely asymptotically Friedmann at large distances. We find eight classes of asymptotic behavior: Friedmann or quasi-Friedmann or quasistatic or constant-velocity at large distances, quasi-Friedmann or positive-mass singular or negative-mass singular at small distances, and quasi-Kantowski-Sachs at intermediate distances. The self-similar asymptotically quasistatic and quasi-Kantowski-Sachs solutions are analytically extendible and of great cosmological interest. We also investigate their conformal diagrams. The results of the present analysis are utilized in an accompanying paper to obtain and physically interpret numerical solutions.

DOI： 10.1103/PhysRevD.77.024022

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state p=(gamma - 1)mu with 0 &lt; gamma &lt; 2/3. This corresponds to a "dark energy" fluid and the Friedmann solution is accelerated in this case due to antigravity. This extends the previous analysis of spherically symmetric self-similar solutions for fluids with positive pressure (gamma &gt; 1). However, in the latter case there is an additional parameter associated with the weak discontinuity at the sonic point and the solutions are only asymptotically "quasi-Friedmann," in the sense that they exhibit an angle deficit at large distances. In the 0 &lt; gamma &lt; 2/3 case, there is no sonic point and there exists a one-parameter family of solutions which are genuinely asymptotically Friedmann at large distances. We find eight classes of asymptotic behavior: Friedmann or quasi-Friedmann or quasistatic or constant-velocity at large distances, quasi-Friedmann or positive-mass singular or negative-mass singular at small distances, and quasi-Kantowski-Sachs at intermediate distances. The self-similar asymptotically quasistatic and quasi-Kantowski-Sachs solutions are analytically extendible and of great cosmological interest. We also investigate their conformal diagrams. The results of the present analysis are utilized in an accompanying paper to obtain and physically interpret numerical solutions.

DOI： 10.1103/PhysRevD.77.024022

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We use a combination of numerical and analytical methods, exploiting the equations derived in a preceding paper, to classify all spherically symmetric self-similar solutions which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state p=(gamma-1)mu with 0 &lt; gamma &lt; 2/3. The expansion of the Friedmann universe is accelerated in this case. We find a one-parameter family of self-similar solutions representing a black hole embedded in a Friedmann background. This suggests that, in contrast to the positive pressure case, black holes in a universe with dark energy can grow as fast as the Hubble horizon if they are not too large. There are also self-similar solutions which contain a central naked singularity with negative mass and solutions which represent a Friedmann universe connected to either another Friedmann universe or some other cosmological model. The latter are interpreted as self-similar cosmological white hole or wormhole solutions. The throats of these wormholes are defined as two-dimensional spheres with minimal area on a spacelike hypersurface and they are all nontraversable because of the absence of a past null infinity.

DOI： 10.1103/PhysRevD.77.024023

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Language：English   Publishing type：Research paper (international conference proceedings)  

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Language：English   Publishing type：Research paper (international conference proceedings)  

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IOP PUBLISHING LTD  

DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) is the future Japanese space gravitational wave antenna. DECIGO is expected to open a new window of observation for gravitational wave astronomy especially between 0.1 Hz and 10 Hz, revealing various mysteries of the universe such as dark energy, formation mechanism of supermassive black holes, and inflation of the universe. The pre-conceptual design of DECIGO consists of three drag-free spacecraft, whose relative displacements are measured by a differential Fabry-Perot Michelson interferometer. We plan to launch two missions, DECIGO pathfinder and pre-DECIGO first and finally DECIGO in 2024.

DOI： 10.1088/1742-6596/120/3/032004

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Language：English   Publishing type：Research paper (international conference proceedings)  

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

We calculate the quantum radiation power of black holes which are asymptotic to the Einstein - de Sitter universe at spatial and null infinities. We consider two limiting mass accretion scenarios, no accretion and significant accretion. We find that the radiation power strongly depends on not only the asymptotic condition but also the mass accretion scenario. For the no accretion case, we consider the Einstein - Straus solution, where a black hole of constant mass resides in the dust Friedmann universe. We find negative cosmological correction besides the expected redshift factor. This is given in terms of the cubic root of ratio in size of the black hole to the cosmological horizon, so that it is currently of order 10(-5)( M/10(6)M(circle dot))(1/3)(t/14Gyr)(-1/3) but could have been significant at the formation epoch of primordial black holes. Due to the cosmological effects, this black hole has not settled down to an equilibrium state. This cosmological correction may be interpreted in an analogy with the radiation from a moving mirror in a flat spacetime. For the significant accretion case, we consider the Sultana - Dyer solution, where a black hole tends to increase its mass in proportion to the cosmological scale factor. In this model, we find that the radiation power is apparently the same as the Hawking radiation from the Schwarzschild black hole of which mass is that of the growing mass at each moment. Hence, the energy loss rate decreases and tends to vanish as time proceeds. Consequently, the energy loss due to evaporation is insignificant compared to huge mass accretion onto the black hole. Based on this model, we propose a definition of quasi- equilibrium temperature for general conformal stationary black holes.

DOI： 10.1088/0264-9381/24/18/011

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Language：English   Publishing type：Research paper (scientific journal)  

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Language：Japanese   Publishing type：Research paper (scientific journal)  

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE  

The gravitational collapse of a thick cylindrical shell of dust matter is investigated. It is found that a spacetime singularity forms on the symmetry axis and that it is necessarily naked, i.e., observable in principle. We propose a physically reasonable boundary condition at this naked singularity to construct the solution including its causal future. This boundary condition enables us to construct the unique continuation of spacetime beyond the naked singularity and ensures that the dust shell passes through the naked singularity. When the cylindrical shell leaves its symmetry axis away, the naked singularity disappears, and regularity is recovered. We construct numerical solutions with this feature. This result implies that the gravity produced by a thick cylindrical shell of dust is too weak to bind the shell even if it engenders the formation of a curvature singularity which is so strong as to satisfy the limiting focusing condition. For this reason, this naked singularity is very weak in the extended spacetime; the metric tensor is C1- even at the naked singularity, and the extended spacetime is complete for almost all geodesics. This feature is also seen for singular hypersurfaces. Such an extended spacetime can be regarded as phenomenological in the sense that it is valid if the relevant microphysics length scale is sufficiently small compared to the scale of interest.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMERICAN PHYSICAL SOC  

Applying the first and generalized second laws of thermodynamics for a realistic process of near critical black hole formation, we derive an entropy bound, which is identical to Bekenstein's one for radiation. Relying upon this bound, we derive an absolute minimum mass similar to 0.04 root g(*)m(Pl), where g(*) and m(Pl) is the effective degrees of freedom for the initial temperature and the Planck mass, respectively. Since this minimum mass coincides with the lower bound on masses of which black holes can be regarded as classical against the Hawking evaporation, the thermodynamical argument will not prohibit the formation of the smallest classical black hole. For more general situations, we derive a minimum mass, which may depend on the initial value for entropy per particle. For primordial black holes, however, we show that this minimum mass can not be much greater than the Planck mass at any formation epoch of the Universe, as long as g(*) is within a reasonable range. We also derive a size-independent upper bound on the entropy density of a stiff fluid in terms of the energy density.

DOI： 10.1103/PhysRevD.74.084004

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We consider the possible existence of self-similar solutions containing black holes in a Friedmann background with a stiff fluid or a scalar field. We carefully study the relationship between the self-similar equations in these two cases and emphasize the crucial role of the similarity horizon. We show that there is no self-similar black hole solution surrounded by an exact or asymptotically flat Friedmann background containing a massless scalar field. This result also applies for a scalar field with a potential, providing the universe is decelerating. However, if there is a potential and the universe is accelerating (as in the quintessence scenario), the result only applies for an exact Friedmann background. This extends the result previously found in the stiff fluid case and strongly suggests that accretion onto primordial black holes is ineffective even during scalar field domination. It also contradicts recent claims that such black holes can grow appreciably by accreting quintessence. Appreciable growth might be possible with very special matter fields but this requires ad hoc and probably unphysical conditions.

DOI： 10.1103/PhysRevD.74.024024

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) is the future Japanese space gravitational wave antenna. It aims at detecting various kinds of gravitational waves between 1 mHz and 100 Hz frequently enough to open a new window of observation for gravitational wave astronomy. The preconceptual design of DECIGO consists of three drag-free satellites, 1000 km apart from each other, whose relative displacements are measured by a Fabry-Perot Michelson interferometer. We plan to launch DECIGO in 2024 after a long and intense development phase, including two pathfinder missions for verification of required technologies.

DOI： 10.1088/0264-9381/23/8/S17

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Language：English   Publishing type：Research paper (international conference proceedings)  

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Language：English   Publishing type：Research paper (scientific journal)  

We consider the possible existence of self-similar solutions containing black holes in a Friedmann background with a stiff fluid or a scalar field. We carefully study the relationship between the self-similar equations in these two cases and emphasize the crucial role of the similarity horizon. We show that there is no self-similar black hole solution surrounded by an exact or asymptotically flat Friedmann background containing a massless scalar field. This result also applies for a scalar field with a potential, providing the universe is decelerating. However, if there is a potential and the universe is accelerating (as in the quintessence scenario), the result only applies for an exact Friedmann background. This extends the result previously found in the stiff fluid case and strongly suggests that accretion onto primordial black holes is ineffective even during scalar field domination. It also contradicts recent claims that such black holes can grow appreciably by accreting quintessence. Appreciable growth might be possible with very special matter fields but this requires ad hoc and probably unphysical conditions. © 2006 The American Physical Society.

DOI： 10.1103/PhysRevD.74.024024

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We study the spherically symmetric collapse of a perfect fluid using area-radial coordinates. Recently, Giambò et al. derived a second-order quasi-linear partial differential equation for the mass function. They claimed that singularities formed in the collapse are naked if the mass function is analytic with respect to the area-radial coordinates in the neighborhood of the singularities. We point out limitations of the analytic mass functions, propose new expressions for the mass function and investigate the relationship between those and the nature of the singularities. © 2006 American Institute of Physics.

DOI： 10.1063/1.2399637

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IOP PUBLISHING LTD  

Primordial black holes have important observational implications through Hawking evaporation and gravitational radiation as well as being a candidate for cold dark matter. Those black holes may have formed in the early universe typically with the mass scale contained within the Hubble horizon at the formation epoch and subsequently accreted the mass surrounding them. Numerical relativity simulation shows that primordial black holes of different masses do not accrete much, which contrasts with a simplistic Newtonian argument. Primordial black holes larger than the cosmological horizon have non-standard global structure, suggesting that they may have formed in inflationary cosmology.

DOI： 10.1088/1742-6596/31/1/019

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We discuss a new class of solutions to the Einstein equations which describe a primordial black hole (PBH) in a flat Friedmann background. Such solutions arise if a Schwarzschild black hole is patched onto a Friedmann background via a transition region. They are possible providing the black hole event horizon is larger than the cosmological apparent horizon. Such solutions have a number of strange features. In particular, one has to define the black hole and cosmological horizons carefully and one then finds that the mass contained within the black hole event horizon decreases when the black hole is larger than the Friedmann cosmological apparent horizon, although its area always increases. These solutions involve two distinct future null infinities and are interpreted as the conversion of a white hole into a black hole. Although such solutions may not form from gravitational collapse in the same way as standard PBHs, there is nothing unphysical about them, since all energy and causality conditions are satisfied. Their conformal diagram is a natural amalgamation of the Kruskal diagram for the extended Schwarzschild solution and the conformal diagram for a black hole in a flat Friedmann background. In this paper, such solutions are obtained numerically for a spherically symmetric universe containing a massless scalar field, but it is likely that they exist for more general matter fields and less symmetric systems. © 2005 The American Physical Society.

DOI： 10.1103/PhysRevD.72.044021

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We discuss a new class of solutions to the Einstein equations which describe a primordial black hole (PBH) in a flat Friedmann background. Such solutions arise if a Schwarzschild black hole is patched onto a Friedmann background via a transition region. They are possible providing the black hole event horizon is larger than the cosmological apparent horizon. Such solutions have a number of strange features. In particular, one has to define the black hole and cosmological horizons carefully and one then finds that the mass contained within the black hole event horizon decreases when the black hole is larger than the Friedmann cosmological apparent horizon, although its area always increases. These solutions involve two distinct future null infinities and are interpreted as the conversion of a white hole into a black hole. Although such solutions may not form from gravitational collapse in the same way as standard PBHs, there is nothing unphysical about them, since all energy and causality conditions are satisfied. Their conformal diagram is a natural amalgamation of the Kruskal diagram for the extended Schwarzschild solution and the conformal diagram for a black hole in a flat Friedmann background. In this paper, such solutions are obtained numerically for a spherically symmetric universe containing a massless scalar field, but it is likely that they exist for more general matter fields and less symmetric systems.

DOI： 10.1103/PhysRevD.72.044021

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The evolution of primordial black holes in a flat Friedmann universe with a massless scalar field is investigated in fully general relativistic numerical relativity. A primordial black hole is expected to form with a scale comparable to the cosmological apparent horizon, in which case it may go through an initial phase with significant accretion. However, if it is very close to the cosmological apparent horizon size, the accretion is suppressed due to general relativistic effects. In any case, it soon gets smaller than the cosmological horizon and thereafter it can be approximated as an isolated vacuum solution with decaying mass accretion. In this situation the dynamical and inhomogeneous scalar field is typically equivalent to a perfect fluid with a stiff equation of state p = rho. The black hole mass never increases by more than a factor of 2, despite recent claims that primordial black holes might grow substantially through accreting quintessence. It is found that the gravitational memory scenario, proposed for primordial black holes in Brans-Dicke and scalar-tensor theories of gravity, is highly unphysical.

DOI： 10.1103/PhysRevD.71.104010

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We provide precise constraints on the size of any black holes forming in the early Universe for a variety of formation scenarios. In particular, we prove that the size of the apparent horizon of a primordial black hole formed by causal processes in a flat Friedmann universe is considerably smaller than the cosmological apparent horizon size for an equation of state p = k rho (1/3 &lt; k &lt; 1). This also applies for a stiff equation of state (k = 1) or for a massless scalar field. The apparent horizon of a primordial black hole formed through hydrodynamical processes is also considerably smaller than the cosmological apparent horizon for 0 &lt; k &lt;= 1. We derive an expression for the maximum size which an overdense region can have without being a separate closed universe rather than part of our own. Newtonian argument shows that a black hole smaller than the cosmological horizon can never accrete much.

DOI： 10.1103/PhysRevD.71.104009

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society  

The evolution of weak discontinuity is investigated on horizons in the n-dimensional static solutions in the Einstein-Maxwell-scalar-Λ system, including the Reissner-Nordström-(anti) de Sitter black hole. The analysis is essentially local and nonlinear. We find that the Cauchy horizon is unstable, whereas both the black hole event horizon and the cosmological event horizon are stable. This new instability, the so-called kink instability, of the Cauchy horizon is completely different from the well-known "infinite- blueshift" instability. The kink instability makes the analytic continuation beyond the Cauchy horizon unstable. © 2005 The American Physical Society.

DOI： 10.1103/PhysRevD.71.064015

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

The evolution of weak discontinuity is investigated on horizons in the n-dimensional static solutions in the Einstein-Maxwell-scalar-Lambda system, including the Reissner-Nordstrom-(anti) de Sitter black hole. The analysis is essentially local and nonlinear. We find that the Cauchy horizon is unstable, whereas both the black hole event horizon and the cosmological event horizon are stable. This new instability, the so-called kink instability, of the Cauchy horizon is completely different from the well-known "infinite-blueshift" instability. The kink instability makes the analytic continuation beyond the Cauchy horizon unstable.

DOI： 10.1103/PhysRevD.71.064015

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE  

There are many solutions to the Einstein field equations that demonstrate naked singularity (NS) formation after regular evolution. It is possible, however, that such a quantum effect as particle creation prevents NSs from forming. We investigate the relation between the curvature strength and the quantum effects of NSs in a very wide class of spherical dust collapse. Through a perturbative calculation, we find that if the NS is very strong, the quantum particle creation diverges as the Cauchy horizon is approached, while if,the NS is very weak, the creation should be finite. In the context of cosmic censorship, strong NSs will be subjected to the backreaction of quantum effects and may disappear or be hidden behind horizons, while weak NSs will not.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

We study the spherically symmetric collapse of a perfect fluid using area-radial coordinates. We show that analytic mass functions describe a static regular centre in these coordinates. In this case, a central singularity cannot be realized without an infinite discontinuity in the central density. We construct mass functions involving fluid dynamics at the centre and investigate the relationship between those and the nature of the singularities.

DOI： 10.1088/0264-9381/22/5/006

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

The evolution of weak discontinuity is investigated in the flat FRW universe with a single scalar field and with multiple scalar fields. We consider both massless scalar fields and scalar fields with exponential potentials. Then we find that a new type of instability, i.e., kink instability develops in the flat FRW universe with massless scalar fields. The kink instability develops with scalar fields with considerably steep exponential potentials, while less steep exponential potentials do not suffer from kink instability. In particular, assisted inflation with multiple scalar fields does not suffer from kink instability. The stability of general spherically symmetric self-similar solutions is also discussed. (C) 2004 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.physletb.2004.12.035

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：KOREAN PHYSICAL SOC  

A stability criterion is derived in general relativity for self-similar solutions with a scalar field and those with a stiff fluid, which is a perfect fluid with the equation of state P = rho. A wide class of self-similar solutions turns out to be unstable against kink mode perturbation. According to the criterion, the Evans-Coleman stiff-fluid solution is unstable and cannot be a critical solution for the spherical collapse of a stiff fluid, if we allow a sufficiently small discontinuity in the density gradient field in the initial data sets. The self-similar scalar-field solution, which was recently found numerically by Brady et al., is also unstable. Both the flat Friedmann universe with a scalar field and that with a stiff fluid suffer from kink instability at the particle horizon scale.

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Language：English   Publishing type：Research paper (international conference proceedings)  

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Generic spherically symmetric self-similar collapse results in strong naked-singularity formation. In this paper we are concerned with particle creation during naked-singularity formation in spherically symmetric self-similar collapse without specifying the collapsing matter. In the generic case, the power of particle emission is found to be proportional to the inverse square of the remaining time to the Cauchy horizon (CH). The constant of proportion can be arbitrarily large in the limit of a marginally naked singularity. Therefore, the unbounded power is especially striking in the case in which an event horizon is very close to the CH, because the emitted energy can be arbitrarily large in spite of the cutoff expected from quantum gravity. The above results suggest the instability of the CH in spherically symmetric self-similar spacetime from quantum field theory and seem to support the existence of a semiclassical cosmic censor. The divergence of redshifts and blueshifts of emitted particles is found to cause the divergence of power to positive or negative infinity, depending on the coupling manner of the scalar fields to gravity. On the other hand, it is found that there is a special class of self-similar spacetimes in which the semiclassical instability of the CH is not efficient. The analyses in this paper are based on the geometric optics approximation, which is justified in two dimensions but needs justification in four dimensions.

DOI： 10.1103/PhysRevD.69.104005

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We consider the possibilities for obtaining information about the equation of state for quark matter by using future direct observational data on gravitational waves. We study the nonradial oscillations of both fluid and spacetime modes of pure quark stars. If we observe the f and the lowest w(II) modes from quark stars, by using the simultaneously obtained radiation radius we can constrain the bag constant B with reasonable accuracy, independently of the s quark mass.

DOI： 10.1103/PhysRevD.69.084008

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Language：Japanese   Publishing type：Research paper (scientific journal)  

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It is still uncertain whether the cosmic censorship conjecture is true or not. To get a new insight into this issue, we propose the concept of the border of spacetime as a generalization of the spacetime singularity and discuss its visibility. The visible border, corresponding to the naked singularity, is not only relevant to mathematical completeness of general relativity but also a window into new physics in strongly curved spacetimes, which is in principle observable. © 2004 The American Physical Society.

DOI： 10.1103/PhysRevD.70.041501

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Generic spherically symmetric self-similar collapse results in strong naked-singularity formation. In this paper we are concerned with particle creation during naked-singularity formation in spherically symmetric self-similar collapse without specifying the collapsing matter. In the generic case, the power of particle emission is found to be proportional to the inverse square of the remaining time to the Cauchy horizon (CH). The constant of proportion can be arbitrarily large in the limit of a marginally naked singularity. Therefore, the unbounded power is especially striking in the case in which an event horizon is very close to the CH, because the emitted energy can be arbitrarily large in spite of the cutoff expected from quantum gravity. The above results suggest the instability of the CH in spherically symmetric self-similar spacetime from quantum field theory and seem to support the existence of a semiclassical cosmic censor. The divergence of redshifts and blueshifts of emitted particles is found to cause the divergence of power to positive or negative infinity, depending on the coupling manner of the scalar fields to gravity. On the other hand, it is found that there is a special class of self-similar spacetimes in which the semiclassical instability of the CH is not efficient. The analyses in this paper are based on the geometric optics approximation, which is justified in two dimensions but needs justification in four dimensions. © 2004 The American Physical Society.

DOI： 10.1103/PhysRevD.69.104005

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE  

We give a classification of spherically symmetric kinematic self-similar solutions. This classification is complementary to that given in a previous work by the present authors [Prog. Theor. Phys. 108 (2002), 819]. Dust solutions of the second, zeroth and infinite kinds, perfect-fluid solutions and vacuum solutions of the first kind are treated. The kinematic self-similarity vector is either parallel or orthogonal to the fluid flow in the perfect-fluid and vacuum cases, while the 'tilted' case, i.e., neither parallel nor orthogonal case, is also treated in the dust case. In the parallel case, there are no dust solutions of the second (except when the self-similarity index a is 3/2), zeroth and infinite kinds, and in the orthogonal case, there are no dust solutions of the second and infinite kinds. Except in these cases, the governing equations can be integrated to give exact solutions. It is found that the dust solutions in the tilted case belong to a subclass of the Lema (i) over cap tre-Tolman-Bondi family of solutions for the marginally bound case. The flat Friedmann-Robertson-Walker (FRW) solution is the only dust solution of the second kind with alpha = 3/2 in the tilted and parallel cases and of the zeroth kind in the orthogonal case. The flat, open and closed FRW solutions with p = -mu/3, where p and mu are the pressure and energy density, respectively, are the only perfect-fluid first-kind self-similar solutions in the parallel case, while a new exact solution with p = U, which we call the "singular stiff-fluid solution", is the only such solution in the orthogonal case. The Minkowski solution is the only vacuum first-kind self-similar solution both in the parallel and orthogonal cases. Some important corrections and complements to the authors' previous work are also presented.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Nonspherical stellar collapse to a black hole is one of the most promising gravitational wave sources for gravitational wave detectors. We numerically study gravitational waves from a slightly nonspherical stellar collapse to a black hole in linearized Einstein theory. We adopt a spherically collapsing star as the zeroth-order solution and gravitational waves are computed using perturbation theory on the spherical background. In this paper we focus on the perturbation of odd-parity modes. Using the polytropic equations of state with polytropic indices n(p)=1 and 3, we qualitatively study gravitational waves emitted during the collapse of neutron stars and supermassive stars to black holes from a marginally stable equilibrium configuration. Since the matter perturbation profiles can be chosen arbitrarily, we provide a few types for them. For n(p)=1, the gravitational waveforms are mainly characterized by a black hole quasinormal mode ringing, irrespective of perturbation profiles given initially. However, for n(p)=3, the waveforms depend strongly on the initial perturbation profiles. In other words, the gravitational waveforms strongly depend on the stellar configuration and, in turn, on the ad hoe choice of the functional form of the perturbation in the case of supermassive stars.

DOI： 10.1103/PhysRevD.68.024002

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMERICAN PHYSICAL SOC  

Recently, it has been reported that a candidate for a quark star may have been observed. In this article, we consider quark stars with radiation radii in the reported range. We calculate nonradial oscillations of f, w, and w(II) modes. We find that the dependence of the f mode quasinormal frequency on the bag constant and stellar radiation radius is very strong and different from that of the lowest w(II) mode quasinormal frequency. Furthermore we deduce a new empirical formula between the f mode frequency of gravitational waves and the parameter of the equation of state for quark stars. The observation of gravitational waves both of the f mode and of the lowest w(II) mode would provide a powerful probe for the equation of state of quark matter and the properties of quark stars.

DOI： 10.1103/PhysRevD.68.024019

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We study through numerical simulation the spherical collapse of isothermal gas in Newtonian gravity. We observe a critical behavior which occurs at the threshold of gravitational instability leading to core formation. This was predicted in a previous work by two of the present authors. We describe it in detail in this work. For a given initial density profile, we find a critical temperature T*, which is of the same order as the virial temperature of the initial configuration. For the exact critical temperature, the collapse converges to a self-similar form, the first member in Hunter's family of self-similar solutions. For a temperature close to T*, the collapse first approaches this critical solution. Later on, in the supercritical case (T&lt;T*), the collapse converges to another self-similar solution, which is called the Larson-Penston solution. In the subcritical case (T&gt;T*), the gas bounces and disperses to infinity. We find two scaling laws with respect to \T-T*\: one for the collapsed mass in the supercritical case and the other, which was not predicted before, for the maximum density reached before dispersal in the subcritical case. The value of the critical exponent is measured to be similar or equal to0.11 in the supercritical case, which agrees well with the predicted value similar or equal to0.10567. These critical properties are quite similar to those observed in the collapse of a radiation fluid in general relativity. We study the response of the system to temperature fluctuation and discuss astrophysical implications for the interstellar medium structure and for the star formation process. Newtonian critical behavior is important not only because it provides a simple model for general relativity but also because it is relevant for astrophysical systems such as molecular clouds.

DOI： 10.1103/PhysRevD.67.084003

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Nonspherical stellar collapse to a black hole is one of the most promising gravitational wave sources for gravitational wave detectors. We numerically study gravitational waves from a slightly nonspherical stellar collapse to a black hole in linearized Einstein theory. We adopt a spherically collapsing star as the zeroth-order solution and gravitational waves are computed using perturbation theory on the spherical background. In this paper we focus on the perturbation of odd-parity modes. Using the polytropic equations of state with polytropic indices np= 1 and 3, we qualitatively study gravitational waves emitted during the collapse of neutron stars and supermassive stars to black holes from a marginally stable equilibrium configuration. Since the matter perturbation profiles can be chosen arbitrarily, we provide a few types for them. For np = 1, the gravitational waveforms are mainly characterized by a black hole quasinormal mode ringing, irrespective of perturbation profiles given initially. However, for np=3, the waveforms depend strongly on the initial perturbation profiles. In other words, the gravitational waveforms strongly depend on the stellar configuration and, in turn, on the ad hoc choice of the functional form of the perturbation in the case of supermassive stars. ©2003 The American Physical Society.

DOI： 10.1103/PhysRevD.68.024002

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We investigate particle velocity in (Formula presented)-Minkowski space-time, which is one of the realizations of noncommutative space-time. We emphasize that arrival time analyses by high-energy (Formula presented) rays or neutrinos, which have been considered as powerful tools to restrict the violation of Lorentz invariance, are not effective in detecting space-time noncommutativity. In contrast with these examples, we point out the possibility that low-energy massive particles play an important role in detecting it. © 2002 The American Physical Society.

DOI： 10.1103/PhysRevD.66.105003

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE  

We classify all spherically symmetric spacetimes admitting a kinematic self-similar vector of the second, zeroth or infinite kind. We assume that the perfect fluid obeys either a polytropic equation of state or an equation of state of the form p = Kmu, where p and mu are the pressure and the energy density, respectively, and K is a constant. We study the cases in which the kinematic self-similar vector is not only "tilted" but also parallel or orthogonal to the fluid flow. We find that, in contrast to Newtonian gravity, the polytropic perfect-fluid solutions compatible with kinematic self-similarity are the Friedmann-Robertson-Walker solution and general static solutions. We find three new exact solutions, which we call the dynamical solutions (A) and (B) and the Lambda-cylinder solution.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMERICAN PHYSICAL SOC  

We investigate particle velocity in kappa-Minkowski space-time, which is one of the realizations of noncommutative space-time. We emphasize that arrival time analyses by high-energy gamma rays or neutrinos, which have been considered as powerful tools to restrict the violation of Lorentz invariance, are not effective in detecting space-time noncommutativity. In contrast with these examples, we point out the possibility that low-energy massive particles play an important role in detecting it.

DOI： 10.1103/PhysRevD.66.105003

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMERICAN PHYSICAL SOC  

In cosmological models with a varying gravitational constant, it is not clear whether primordial black holes preserve the value of G at their formation epoch. We investigate this question by using the Tolman-Bondi model to study the evolution of a background scalar field when a black hole forms from the collapse of dust in a flat Friedmann universe. Providing the back reaction of the scalar field on the metric can be neglected, we find that the value of the scalar field at the event horizon very quickly assumes the background cosmological value. This suggests that there is very little gravitational memory.

DOI： 10.1103/PhysRevD.66.104023

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Language：English   Publishing type：Research paper (international conference proceedings)  

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We investigate spherically symmetric spacetimes which contain a perfect fluid obeying the polytropic equation of state and admit a kinematic self-similar vector of the second kind which is neither parallel nor orthogonal to the fluid flow. We assume two kinds of polytropic equations of state and show in general relativity that such spacetimes must be a vacuum, which is in contrast with the result in the Newtonian case.

DOI： 10.1103/PhysRevD.66.027501

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE  

Gravitational collapse is one of the most. fruitful subjects in gravitational physics. It is well known that singularity formation is inevitable in complete gravitational collapse. It was conjectured that such a singularity should be hidden by horizons if it is formed from generic initial data with physically reasonable matter fields. Many possible counterexamples to this conjecture have been proposed over the past three decades, although none of them has proved to be sufficiently generic. In these examples, there appears a singularity that is not hidden by horizons. This singularity is called a 'naked singularity'. The appearance of a naked singularity represents the formation of an observable high-curvature, strong-gravity region. In this paper we review examples of naked singularity formation and recent progress in research of observable physical processes - gravitational radiation and quantum particle creation - from a forming naked singularity.

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We discuss astrophysical implications of κ-Minkowski space-time, in which space-time noncommutativity appears. We first derive a velocity formula for particles based on the motion of a wave packet. The result is that a massless particle moves at a constant speed as in the usual Minkowski space-time, which implies that an arrival time analysis of γ rays from Markarian (Mk) 421 does not exclude space-time noncommutativity. Based on this observation, we analyze reaction processes in κ-Minkowski space-time which are related to the puzzling detection of extremely high-energy cosmic rays above the Greisen-Zatsepin-Kuzmin cutoff and of high-energy (∼20 TeV) γ rays from Mk 501. In these analyses, we take into account the ambiguity of the momentum conservation law which cannot be determined uniquely from a mathematical viewpoint. We find that peculiar types of momentum conservation law with some length scale of noncommutativity above a critical length scale can explain such puzzling detection. We also obtain stringent constraints on the length scale of noncommutativity and the freedom of the momentum conservation law. © 2002 The American Physical Society.

DOI： 10.1103/PhysRevD.65.083003

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A stability criterion is derived for self-similar solutions with perfect fluids which obey the equation of state P = kp in general relativity. A wide class of self-similar solutions turn out to be unstable against the so-called kink mode. The criterion is directly related to the classification of sonic points. The criterion gives a sufficient condition for instability of the solution. For a transonic point in collapse, all primary-direction nodal-point solutions are unstable, while all secondary-direction nodal-point solutions and saddle-point ones are stable against the kink mode. The situation is reversed in expansion. The applications are the following: the expanding flat Friedmann solution for 1/3 ≤ k &lt
1 and the collapsing one for 0 &lt
k ≤ 1/3 are unstable
the static self-similar solution is unstable
nonanalytic self-similar collapse solutions are unstable
the Larson-Penston (attractor) solution is stable for this mode for 0 &lt
k ≲ 0.036, while it is unstable for 0.036 ≲ k
the Evans-Coleman (critical) solution is stable for this mode for 0 &lt
k ≲ 0.89, while it is unstable for 0.89 ≲ k. The last application suggests that the Evans-Coleman solution for 0.89 ≲ k is not critical because it has at least two unstable modes.

DOI： 10.1088/0264-9381/18/21/311

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

A stability criterion is derived for self-similar solutions with perfect fluids which obey the equation of state P = k rho in general relativity. A wide class of selfsimilar solutions turn out to be unstable against the so-called kink made. The criterion is directly related to the classification of sonic points. The criterion gives a sufficient condition for instability of the solution. For a transonic point in collapse, all primary-direction nodal-point solutions are unstable, while all secondary-direction nodal-point solutions and saddle-point ones are stable against the kink mode. The situation is reversed in expansion. The applications are the following: the expanding flat Friedmann solution for 1/3 less than or equal to k &lt; 1 and the collapsing one for 0 &lt; k less than or equal to 1/3 are unstable; the static self-similar solution is unstable; nonanalytic self-similar collapse solutions are unstable; the Larson-Penston (attractor) solution is stable for this mode for 0 &lt; k less than or similar to 0.036, while it is unstable for 0.036 less than or similar to k; the Evans-Coleman (critical) solution is stable for this mode for 0 &lt; k less than or similar to 0.89, while it is unstable for 0.89 k. The last application suggests that the Evans-Coleman solution for 0.89 less than or similar to k is not critical because it has at least two unstable modes.

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The behaviour of the quantum stress tensor for the scalar field on the classical background of a spherical dust collapse is studied. In previous works a diverging flux of quantum radiation was predicted. We use the exact expressions in a two-dimensional model formulated by Barve et al (1998 Phys. Rev. D 58 104018). Our present results show that the backreaction does not become important during the semiclassical phase. The appearance of the naked singularity would not be affected by this quantum field radiation. To predict whether or not explosion of the naked singularity occurs, we need a theory of quantum gravity. We depict the generation of a diverging flux inside the collapsing star. The quantum energy is gathered around the centre positively. This would be converted into a diverging flux along the Cauchy horizon. The ingoing negative flux crosses the Cauchy horizon. The intensity of it is divergent only at the central naked singularity. This diverging negative ingoing flux is balanced with the outgoing positive diverging flux which propagates along the Cauchy horizon. After replacement of the naked singularity by a practical high-density region, the instantaneous diverging radiation would change to a milder one with finite duration.

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DOI： 10.1103/PhysRevD.63.084003

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We study the spherical collapse of a perfect fluid with an equation of state (Formula presented) by full general relativistic numerical simulations. For (Formula presented) it has been known that there exists a general relativistic counterpart of the Larson-Penston self-similar Newtonian solution. The numerical simulations strongly suggest that, in the neighborhood of the center, generic collapse converges to this solution in an approach to a singularity and that self-similar solutions other than this solution, including a “critical solution” in the black hole critical behavior, are relevant only when the parameters which parametrize initial data are fine-tuned. This result is supported by a mode analysis on the pertinent self-similar solutions. Since a naked singularity forms in the general relativistic Larson-Penston solution for (Formula presented) this will be the most serious known counterexample against cosmic censorship. It also provides strong evidence for the self-similarity hypothesis in general relativistic gravitational collapse. The direct consequence is that critical phenomena will be observed in the collapse of isothermal gas in Newton gravity, and the critical exponent (Formula presented) will be given by (Formula presented) though the order parameter cannot be the black hole mass. © 2001 The American Physical Society.

DOI： 10.1103/PhysRevD.63.084022

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We study the spherical collapse of a perfect fluid with an equation of state P = kp by full general relativistic numerical simulations. For 0&lt
Jt:£0.036, it has been known that there exists a general relativistic counterpart of the Larson-Penston self-similar Newtonian solution. The numerical simulations strongly suggest that, in the neighborhood of the center, generic collapse converges to this solution in an approach to a singularity and that self-similar solutions other than this solution, including a "critical solution" in the black hole critical behavior, are relevant only when the parameters which parametrize initial data are fine-tuned. This result is supported by a mode analysis on the pertinent self-similar solutions. Since a naked singularity forms in the general relativistic Larson-Penston solution for 0&lt
£:£0.0105, this will be the most serious known counterexample against cosmic censorship. It also provides strong evidence for the self-similarity hypothesis in general relativistic gravitational collapse. The direct consequence is that critical phenomena will be observed in the collapse of isothermal gas in Newton gravity, and the critical exponent y will be given by 7= 0.11, though the order parameter cannot be the black hole mass. ©2001 The American Physical Society.

DOI： 10.1103/PhysRevD.63.084022

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We investigate the stability of self-similar solutions for a gravitationally collapsing isothermal sphere in Newtonian gravity by means of a normal mode analysis. It is found that the Hunter series of solutions are highly unstable, while neither the Larson-Penston solution nor the homogeneous collapse solution has an analytic unstable mode. Since the homogeneous collapse solution is known to suffer the kink instability, the present result and recent numerical simulations strongly support a proposition that the Larson-Penston solution will be realized in astrophysical situations. It is also found that the Hunter (A) solution has a single unstable mode, which implies that it is a critical solution associated with some critical phenomena which are analogous to those in general relativity. The critical exponent (Formula presented) is calculated as (Formula presented) In contrast with the general relativistic case, the order parameter will be the collapsed mass. In order to obtain a complete picture of the Newtonian critical phenomena, full numerical simulations will be needed. © 2001 The American Physical Society.

DOI： 10.1103/PhysRevD.64.124024

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There are known models of spherical gravitational collapse in which the collapse ends in a naked shell-focusing singularity for some initial data. If a massless scalar field is quantized on the classical background provided by such a star, it is found that the outgoing quantum flux of the scalar field diverges in the approach to the Cauchy horizon. We argue that the semiclassical approximation (i.e., quantum field theory on a classical curved background) used in these analyses ceases to be valid about one Planck time before the epoch of naked singularity formation, because by then the curvature in the central region of the star reaches the Planck scale. It is shown that during the epoch in which the semiclassical approximation is valid, the total emitted energy is about one Planck unit, and is not divergent. We also argue that back reaction in this model does not become important so long as gravity can be treated classically. It follows that the further evolution of the star will be determined by quantum gravitational effects, and without invoking quantum gravity it is not possible to say whether the star radiates away on a short time scale or settles down into a black hole state. ©2001 The American Physical Society.

DOI： 10.1103/PhysRevD.64.041501

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A direct method is developed to reconstruct the equation of state for high-density nuclear matter from the relationship between any two properties of neutron stars, such as masses, radii, moments of inertia, baryonic masses, binding energies, gravitational redshifts, and their combinations. © 2001 The American Physical Society.

DOI： 10.1103/PhysRevC.64.048801

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We rigorously analyze the frequency response functions and antenna sensitivity patterns of three types of interferometric detectors to the scalar mode of gravitational waves which is predicted to exist in the scalar-tensor theory of gravity. By a straightforward treatment, we show that the antenna sensitivity pattern of the simple Michelson interferometric detector depends strongly on the wavelength (Formula presented) of the scalar mode of the gravitational waves if (Formula presented) is comparable to an arms length of the interferometric detector. For the Delay-Line and Fabry-Perot interferometric detectors with an arms length much shorter than (Formula presented) however, the antenna sensitivity patterns depend weakly on (Formula presented) even though (Formula presented) is comparable to the effective path length of those interferometers. This agrees with the result obtained by Maggiore and Nicolis. © 2001 The American Physical Society.

DOI： 10.1103/PhysRevD.63.082001

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A naked singularity occurs in the generic collapse of an inhomogeneous dust ball. We study the even-parity mode of gravitational waves from a naked singularity of the Lemaitre-Tolman-Bondi spacetime. The wave equations for gravitational waves are solved by numerical integration using the single null coordinate. The result implies that the metric perturbation grows when it approaches the Cauchy horizon and diverges there, although the naked singularity is not a strong source of even-parity gravitational radiation. Therefore, the Cauchy horizon in this spacetime should be unstable with respect to linear even-parity perturbations.

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We investigate the causal structure of the Harada-Iguchi-Nakao (HIN)’s exact solution in detail, which describes the dynamical formation of a naked singularity in the collapse of a regular spherical cluster of counterrotating particles. There are three kinds of radial null geodesics in the HIN spacetime. One is the regular null geodesics and the other two are the null geodesics which terminate at the singularity. The central massless singularity is a timelike naked singularity and satisfies the strong curvature condition along the null geodesics except for the instant of singularity formation. The cluster dynamically asymptotes to the singular static Einstein cluster in which the centrifugal force is balanced with gravity. The HIN solution provides an interesting example which demonstrates that collisionless particles invoke a timelike naked singularity. © 2000 The American Physical Society.

DOI： 10.1103/PhysRevD.62.104016

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It is known that the gravitational collapse of a dust ball results in naked singularity formation from an initial density profile which is physically reasonable. In this paper, we show that explosive radiation is emitted during the formation process of the naked singularity. © 2000 The American Physical Society.

DOI： 10.1103/PhysRevD.61.101502

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Language：English   Publishing type：Research paper (scientific journal)  

It is well known that a naked singularity occurs in the gravitational collapse of an inhomogeneous dust ball from an initial density profile which is physically reasonable. In this paper we show that explosive radiation is emitted during the formation process of the naked singularity while we fix the background spacetime. The energy flux is proportional to (Formula presented) for a minimally coupled massless scalar field, while it is proportional to (Formula presented) for a conformally coupled massless scalar field, where (Formula presented) is the “remaining time” until the distant observer could observe the singularity if the naked singularity was formed. As a consequence, the radiated energy grows unboundedly for both scalar fields. The amount of the power and energy depends on the parameters which characterize the initial density profile but do not depend on the gravitational mass of the cloud. In particular, there is a characteristic frequency (Formula presented) of the singularity above which the divergent energy is radiated. The energy flux is dominated by particles of which the wavelength is about (Formula presented) at each moment. The observed total spectrum is nonthermal, i.e., (Formula presented) for (Formula presented) If the naked singularity formation could continue until a considerable fraction of the total energy of the dust cloud is radiated, the radiated energy would reach about (Formula presented) The calculations are based on the geometrical optics approximation which turns out to be consistent for a rough order estimate. The analysis does not depend on whether or not the naked singularity occurs in its exact meaning. This phenomenon may provide a new candidate for a source of ultrahigh energy cosmic rays or a central engine of (Formula presented)-ray bursts. © 2000 The American Physical Society.

DOI： 10.1103/PhysRevD.62.084037

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Language：English   Publishing type：Research paper (international conference proceedings)  

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

It was shown recently that the metric functions which describe a spherically symmetric spacetime with vanishing radial pressure can be explicitly integrated. We investigate the nakedness and curvature strength of the shell-focusing singularity in that spacetime. If the singularity is naked, the relation between the circumferential radius and the Misner-Sharp mass is given by R approximate to 2y(0)m(B) with 1/3 &lt; beta less than or equal to 1 along the first radial null geodesic from the singularity. The beta is closely related to the: curvature strength of the naked singularity. For example, for the outgoing or ingoing null geodesic, if the strong curvature condition (SCC) of Tipler holds, then beta must be equal to 1. We define the 'gravity-dominance condition' (GDC) for a geodesic. If GDC is satisfied for the null geodesic, both SCC and the limiting focusing condition (LFC) of Krolak holds for beta = 1 and y(0) not equal 1, not SCC but only LFC holds for 1/2 less than or equal to beta &lt; 1, and neither holds for 1/3 &lt; beta &lt; 1/2, for the null geodesic. On the other hand, if GDC is satisfied for the timelike geodesic r = 0, both SCC and LFC are satisfied for the timelike geodesic, irrespective of the value of beta. Several examples are also discussed.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE  

It has been suggested that a naked singularity is a good candidate for a strong gravitational wave burster. A naked singularity occurs in the generic collapse of an inhomogeneous dust ball. We study the odd-parity mode of gravitational waves from a naked singularity of the Lemaitre-Tolman-Bondi spacetime. The wave equation for gravitational waves is solved by numerical integration using the single null coordinate. It is found that the naked singularity is not a strong source of the odd-parity gravitational radiation, although the metric perturbation grows in the central region. Therefore, the Cauchy horizon in this spacetime should be marginally stable with respect to odd-parity perturbations.

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Language：English   Publishing type：Doctoral thesis  

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Language：English   Publishing type：Research paper (other academic)  

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Language：English   Publishing type：Research paper (scientific journal)  

The relation between the angular diameter distance and redshift (Formula presented) relation) in a spherically symmetric dust-shell universe is studied. We discover that the relation agrees with that of an appropriate Friedmann-Lemaître (FL) model if we set a “homogeneous” expansion law and a “homogeneous” averaged density field. This will support the averaging hypothesis that a universe looks similar to a FL model in spite of small-scale fluctuations of density field, if its averaged density field is homogeneous on large scales. We also study the connection of the proper mass of a shell with the mass of gravitationally bound objects. Combining this with the results of the (Formula presented) relation, we discuss an impact of the local inhomogeneities on the determination of the cosmological parameters through the observation of the locally inhomogeneous universe. © 1999 The American Physical Society.

DOI： 10.1103/PhysRevD.60.103508

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Language：English   Publishing type：Research paper (international conference proceedings)  

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Language：English   Publishing type：Research paper (scientific journal)  

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Language：English   Publishing type：Research paper (scientific journal)  

The relation between the angular diameter distance and redshift (Formula presented) relation) in a spherically symmetric dust-shell universe is studied. This model has large inhomogeneities of matter distribution on small scales. We have discovered that the relation agrees with that of an appropriate Friedmann-Lemaître (FL) model if we set a “homogeneous” expansion law and a “homogeneous” averaged density field. This will support the averaging hypothesis that a universe looks like a FL model in spite of small-scale fluctuations of density field, if its averaged density field is homogeneous on large scales. © 1998 The American Physical Society.

DOI： 10.1103/PhysRevD.58.103504

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Language：English   Publishing type：Research paper (scientific journal)  

The final fate of the spherically symmetric collapse of a perfect fluid which follows the γ-law equation of state and adiabatic condition is investigated. Full general relativistic hydrodynamics is solved numerically using a retarded time coordinate, the so-called observer time coordinate. Thanks to this coordinate, the causal structure of the resultant space-time is automatically constructed. Then, it is found that a globally naked, shell-focusing singularity can occur at the center from relativistically high-density, isentropic, and time symmetric initial data if (Formula presented) within the numerical accuracy. The result is free from the assumption of self-similarity. The upper limit of γ with which a naked singularity can occur from generic initial data is consistent with the result of Ori and Piran based on the assumption of self-similarity. © 1998 The American Physical Society.

DOI： 10.1103/PhysRevD.58.104015

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Language：English   Publishing type：Research paper (scientific journal)  

The motion of a spherical dust cloud is described by the Lemaître-Tolman-Bondi solution and is completely specified by initial values of distributions of the rest mass density and specific energy of the dust fluid. From generic initial conditions of this spherically symmetric collapse, there appears a naked singularity at the symmetric center in the course of the gravitational collapse of the dust cloud. So this might be a counterexample to the cosmic censorship hypothesis. To investigate the genericity of this example, we examine the stability of the “nakedness” of this singularity against odd-parity modes of non-spherical linear perturbations for the metric, i.e., linear gravitational waves. We find that the perturbations do not diverge but are well-behaved even in the neighborhood of the central naked singularity. This means that the naked singularity formation process is marginally stable against the odd-parity modes of linear gravitational waves. © 1998 The American Physical Society.

DOI： 10.1103/PhysRevD.57.7262

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Language：English   Publishing type：Research paper (scientific journal)  

We investigate neutron stars in scalar-tensor theories. We examine their secular stability against spherically symmetric perturbations by use of a turning point method. For some choices of the coupling function contained in the theories, the number of the stable equilibrium solutions changes and the realized equilibrium solution may change discontinuously as the asymptotic value of the scalar field or total baryon number is changed continuously. The behavior of the stable equilibrium solutions is explained by fold and cusp catastrophes. Whether or not the cusp catastrophe appears depends on the choice of the coupling function. These types of catastrophes are structurally stable. Recently discovered spontaneous scalarization, which is a nonperturbative strong-field phenomenon due to the presence of the gravitational scalar field, is well described in terms of the cusp catastrophe. © 1998 The American Physical Society.

DOI： 10.1103/PhysRevD.57.4802

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Language：English   Publishing type：Research paper (international conference proceedings)  

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：KYOTO UNIV  

A stability analysis of a spherically symmetric star in scalar-tensor theories of gravity is given in terms of the frequencies of quasi-normal modes. The scalar-tensor theories have a scalar field which is related to gravitation. There is an arbitrary function, the so-called coupling function, which determines the strength of the coupling between the gravitational scalar field and matter. Instability is induced by the scalar field for some ranges of the value of the first derivative of the coupling function. This instability leads to significant discrepancies with the results of binary-pulsar-timing experiments and hence, by the stability analysis, we can exclude the ranges of the first derivative of the coupling function in which the instability sets in. In this article, the constraint on the first derivative of the coupling function from the stability of relativistic stars is found. Analysis in terms of the quasi normal mode frequencies accounts for the parameter dependence of the wave form of the scalar gravitational waves emitted from the Oppenheimer-Snyder collapse. The spontaneous scalarization is also discussed.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMERICAN PHYSICAL SOC  

Unlike general relativity, scalar-tensor theories of gravity predict scalar gravitational waves even from a spherically symmetric gravitational collapse. We solve numerically the generation and propagation of the scalar gravitational wave from a spherically symmetric and homogeneous dust collapse under the approximation that we can neglect the back reaction of the scalar wave on the space-time, and examine how the amplitude, characteristic frequency, and wave form of the observed scalar gravitational wave depend on the initial radius and mass of the dust and parameters contained in the theory. In the Brans-Dicke theory, through the observation of the scalar gravitational wave, it is possible to determine the initial radius and mass and a parameter contained in the theory. In the scalar-tensor theories, it would be possible to get the information of the first derivative of the coupling function contained in the theory because the wave form of the scalar gravitational wave greatly depends on it.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE  

We review the current status of researches on scalar-tensor theories of gravity which have been done by our group.

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Language：English   Publishing type：Research paper (international conference proceedings)  

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Language：Japanese   Publishing type：Master’s thesis  

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Language：Japanese   Publishing type：Research paper (other academic)  

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Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (bulletin of university, research institution)  

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Language：English   Publishing type：Other   Publisher：AMER PHYSICAL SOC  

DOI： 10.1103/PhysRevD.86.069902

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Publishing type：Internal/External technical report, pre-print, etc.  

We investigate a trapped surface and naked singularity in a $D$-dimensional
Vaidya spacetime with a self-similar mass function. A trapped surface is
defined as a closed spacelike $(D-2)$-surface which has negative both null
expansions. There is no trapped surface in the Minkowski spacetime. However, in
a four-dimensional self-similar Vaidya spacetime, Bengtsson and Senovilla
considered non-spherical trapped surfaces and showed that a trapped surface can
penetrate into a flat region, if and only if the mass function rises fast
enough [I. Bengtsson and J. M. M. Senovilla, Phys. Rev. D \textbf{79}, 024027
(2009).]. We apply this result to a $D$-dimensional spacetime motivated by the
context of large extra dimensions or TeV-scale gravity. In this paper,
similarly to Bengtsson and Senovilla's study, we match four types of
$(D-2)$-surfaces and show that a trapped surface extended into the flat region
can be constructed in the $D$-dimensional Vaidya spacetime, if the increasing
rate of the mass function is greater than 0.4628. Moreover, we show that the
maximum radius of the trapped surface constructed here approaches the
Schwarzschild-Tangherlini radius in the large $D$ limit. Also, we show that
there is no naked singularity, if the spacetime has the trapped surface
constructed here.

DOI： 10.1088/1742-6596/314/1/012068

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Language：English   Publishing type：Other   Publisher：AMER PHYSICAL SOC  

DOI： 10.1103/PhysRevD.80.109903

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Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (bulletin of university, research institution)  

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Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (bulletin of university, research institution)  

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