arXiv subjects

Yasutaka Koga

Publications and source records attributed to Yasutaka Koga.

At least 19 recordsLinked to original sources

arXiv2026

Odd-parity ringdown gravitational waves of a spherically symmetric black hole with perfect fluid accretion

The ringdown waves from a black hole offer a clean probe of strong-field gravity, but a matter distribution that may be present around a realistic black hole renders the background spacetime dynamical and the ringdown frequencies time-dependent. We study the odd-parity ringdown of a Schwarzschild black hole that grows through the dilute, steady, spherically symmetric accretion of a perfect fluid. Working to first order in the accretion rate, we compute the ringdown waveform directly in the time domain on this dynamical background. Since the odd-parity matter perturbation decouples from the metric perturbation, the wave mode can be described by a purely tensorial mode on the accreting background. In particular, the ratio of the imaginary to the real part of the frequency cancels both the secular variation caused by the growth of the black hole and the redshift factor, so that its deviation from the Schwarzschild value purely reflects the surrounding environment. The time dependence of the frequency, on the other hand, reflects the accretion rate and allows us to define a second observable tied to it. We argue that measuring these observables across multiple modes may provide significant information to constrain the surrounding environment of the black hole.

gr-qc↗

arXiv2026

COSMOS: A numerical relativity code specialized for PBH formation

Primordial black holes (PBHs) are black holes generated in the early universe without having gone through stellar evolution. In the standard formation process, PBHs are formed from super-horizon primordial fluctuations with non-linearly large initial amplitude. In order to simulate the non-linear gravitational dynamics of PBH formation, one has to rely on numerical relativity solvers to approximate the solution of the Einstein equations. COSMOS is a C++ package for solving the Einstein equations in 3+1 dimensions, providing simple tools for the simulation of PBH formation. In order to resolve the collapsing region, non-Cartesian scale-up coordinates and a fixed mesh-refinement procedure are implemented. In COSMOS, a massless scalar field and a perfect fluid with a linear equation of state are implemented as matter fields. To achieve a practically acceptable computational speed, OpenMP is used for the parallelization. COSMOS has no other dependencies, which makes for an easier installation.

gr-qc↗

arXiv2026

Bulk-cone singularities and echoes from AdS exotic compact objects

The region near a black hole horizon may be modified by quantum gravity effects that resolve the singularity. Such geometry may be represented by an exotic compact object. Because the horizon is enclosed by a photon sphere, it is difficult to probe this region directly. In this paper, we develop a method to study the region inside the photon sphere by applying the AdS/CFT correspondence. We extract signatures of the modified geometry from the retarded Green functions of the dual conformal field theory. The retarded Green functions can be computed from bulk wave functions of scalar field. We show that exotic compact objects leave two characteristic imprints: bulk-cone singularities and echoes. The bulk-cone singularities correspond to null geodesics in the bulk, allowing us to detect null trajectories that are specific to exotic compact objects. The echoes arise from wave modes trapped inside the photon sphere, and thus signal the absence of a horizon. As concrete examples, we study AdS gravastar and AdS wormhole. We compute the corresponding bulk wave functions both via the WKB approximation and through numerical analysis and observe the bulk-cone singularities and echoes explicitly.

hep-th↗

arXiv2026

AdS gravastar and its signatures from dual conformal field theory

Quantum gravity effects are expected to resolve the black hole singularity and the effects may deform the region near but outside the horizon. Applying AdS/CFT correspondence, we see their signatures from the viewpoint of dual conformal field theory. As a regularized geometry, we consider AdS gravastar constructed by gluing AdS-Schwarzschild and de Sitter spacetime. The retarded Green functions of dual conformal field theory have bulk-cone singularities associated with null trajectories in the bulk and we obtain the singularities specific to a horizon-less geometry. We also observe echoes coming from waves reflected behind the photon sphere. The existence of echoes implies the modification of geometry inside the photon sphere.

hep-th↗

arXiv2026

Rotating wormholes in five dimensions with equal angular momenta: large asymmetry regime

We clarify the relationship between rotation and the energy condition for stationary rotating wormhole solutions of the Einstein equations coupled to a phantom field in five-dimensional spacetime with equal angular momenta, particularly with large asymmetry between the two sides. It was shown by Dzhunushaliev et al. that the violation of the null energy condition can become arbitrarily small due to rotation. We find that the degree of violation of the null energy condition is essentially determined by the angular momentum and shows little dependence on asymmetry, that is, the mass difference between the two asymptotic regions. We also discuss the relation between the wormhole spacetime and the Myers-Perry black hole. We find that the geometry asymptotes to the extremal Myers-Perry spacetime in the limit of large angular momentum, while the non-extremal black hole geometry cannot be reproduced in any limit.

gr-qc↗

arXiv2026

Dynamical Formation of Self-Similar Wormholes

We study spherically symmetric, self-similar wormhole solutions supported by colliding streams of negative-energy null dust, and their dynamical formation. Under the assumption of self-similarity, the Einstein equations reduce to a system of ordinary differential equations, which we solve numerically under boundary conditions enforcing the existence of a minimal areal radius (the throat) on constant-time hypersurfaces. For a sufficiently large throat radius, the resulting geometries remain regular at both spatial and future null infinity, while a singularity is retained in the past direction. We then construct a dynamical formation scenario by patching together three regions: a Schwarzschild black hole, negative-energy Vaidya spacetimes, and the self-similar wormhole geometry. These regions are joined across null shells using the Barrabes--Israel formalism, which provides explicit relations among the throat radius, the black hole's mass and the energy injection by the shell, demonstrating that an initial black hole can evolve into a wormhole. Our analysis generalizes the formation model for static wormhole solutions proposed by Hayward and Koyama in 2004 to non-static wormhole solutions, offering a novel perspective on the formation of regular traversable wormholes.

gr-qc↗

arXiv2026

Dynamical Formation of Charged Wormholes

We construct static, spherically symmetric, charged traversable wormhole solutions to the Einstein--Maxwell equations, supported by bidirectional (ingoing and outgoing) null dust with negative energy, and discuss a scenario for their dynamical formation from a black hole. Our solution contains a traversable throat, where the areal radius takes a minimum, although the spacetime is not asymptotically flat. In our formation scenario, the spacetime evolves sequentially from a black hole to Vaidya regions and finally to a wormhole, with each transition mediated by an impulsive null shell. We find that the radius of the wormhole throat is determined by the mass and charge of the initial black hole as well as those of the injected shell.

gr-qc↗

arXiv2025

Shadow formation in gravitational collapse: Redshift and blueshift by spacetime dynamics

A black hole illuminated by a background light source is observed as a black hole shadow. For a black hole formed by gravitational collapse of a transmissive object, redshift of light due to the spacetime dynamics is expected to play a crucial role in the shadow formation. In this paper, we investigate the redshift of light caused by the spacetime dynamics. First, we consider a spherical shell model. We see that the collapse of the shell typically leads to the redshift of light, while blueshift can be also observed in some cases. This result suggests that a shadow image is generally formed in the late stage of the gravitational collapse of a transmissive object. Second, we propose a covariant formula for the redshift of light in a general, dynamical, and spherically symmetric spacetime. This formula relates the redshift to the energy-momentum tensor of the background spacetime and provides its intuitive interpretation with a Newtonian analogy. The redshift effect analyzed in this work is regarded as the integrated Sachs-Wolfe effect or the Rees-Sciama effect in gravitational collapse.

gr-qc↗

arXiv2025

AdS gravastar and bulk-cone singularities

The horizon of black hole is surrounded by the photon sphere and an outside observer cannot easily examine the geometry inside the photon sphere. In this note, we propose a way to investigate the region from dual conformal field theory by making use of AdS/CFT correspondence. We first construct gravastar geometry as an asymptotic anti-de Sitter spacetime, where the region inside the photon sphere is replaced by a horizon-less geometry. It is known that bulk-cone singularities in the retarded Green function in dual conformal field theory can encode the bulk null geodesics. We then compute numerically the retarded Green function from the bulk theory and observe bulk-cone singularities corresponding to null geodesics traveling into the interior region. In this way, we show that it is possible to examine the region inside the photon sphere from bulk-cone singularities of dual conformal field theory.

hep-th↗

arXiv2025

Test particle motion around a black hole dressed with a spherically symmetric stationary fluid

We investigate the motion of a massive particle around a spherically symmetric black hole surrounded by a stationary and radial inflow of perfect fluid. The background spacetime is modelled as a spherically symmetric solution to the Einstein field equations, where the effect of the fluid on the geometry is treated as a perturbation on the Schwarzschild background. The equation of state for the fluid is assumed to follow the linear relationship $p = w ρ$, where $p$ is the pressure, $ρ$ is the energy density with $w$ being a constant. The stress-energy tensor is treated as a phenomenological model to capture deviations from the vacuum Einstein theory. We allow the parameter $w$ of the equation of state to take both positive and negative values accepting a broad range of scenarios including exotic ones. Specifically, we examine the cases $w =2/3$, $1/3$, $-3/4$ and $-4/3$. For $ρ\geq0$, the former two cases satisfy all standard energy conditions while the case of $w=-3/4$ violates the strong energy condition and the case of $w=-4/3$ violates all standard energy conditions. By solving the geodesic equations, we visualize the time-like geodesics around the black hole, focusing on the apsis shift of the orbit. To gain further insight into the effects of accretion, we employ the method of osculating orbital elements. Additionally, we analyze the observable effects on spacetime by studying the redshift of the orbiting test particles as an example of possible observables. We show that the difference in the particle orbits due to the matter accretion may be probed by using the redshift observation of stars orbiting around the black hole.

gr-qc↗

arXiv2025

Geometrical origin for the compaction function for primordial black hole formation

We propose a geometrical origin for the Shibata-Sasaki compaction function, which is known to be a reliable indicator of primordial black hole formation at least during radiation domination. In the long-wavelength limit, we identify it with a compactness function in the static spacetime obtained by removing the cosmological scale factor from the metric and this explains why it cannot be greater than $1/2$. If its maximum is below $1/2$, the perturbation is of type I. If its maximum equals $1/2$, it corresponds to an extremal surface, which is simultaneously a bifurcating trapping horizon and admits a circular photon orbit in the static spacetime. In the long-wavelength regime of the physical expanding Universe, the Shibata-Sasaki compaction reaches its maximum value of $1/2$ at maximal and minimal surfaces on the constant time spacelike hypersurface, which feature a type II perturbation and both correspond to photon spheres expanding along with the cosmological expansion. Thus, the Shibata-Sasaki compaction measures how close to the type II configuration the perturbed region is.

gr-qc↗

arXiv2024

Revisiting spins of primordial black holes in a matter-dominated era based on peak theory

We estimate the probability distribution for the spins of the primordial black holes (PBHs) that formed during an early matter-dominated era in the Universe. We employ the Zel'dovich approximation and focus on the linear-order effect of cosmological perturbations which causes the tidal torque. Assuming that the fluctuations obey Gaussian statistics, we apply the peak theory of random Gaussian variables to compute the root mean square (RMS) and the probability distribution of the non-dimensional Kerr parameter $a_{*}$ at their formation. The value of $a_{*}$ is evaluated through the angular momentum at the turn-around time. We find that the RMS $\bar{a}_{*}$ with a given amplitude of the fluctuation $δ_{\rm{pk}}$ decreases with the amplitude. This behavior allows us to set the threshold value of the amplitude of the fluctuation through the under-extremal condition $\bar{a}_{*}<1$. Then we discuss the impact of spin and anisotropic collapse on the production rate of PBHs. We find that, for $σ_{H}\leq 10^{-3}$ with $σ_{\rm H}$ being the square root of the variance of the fluctuation at the horizon reentry, the suppression from the spin effect is dominant, while the effect of anisotropy becomes more important for $σ_{H}>10^{-3}$. Since $\bar{a}_{*}$ can be written as a function of $ν:=δ_{\rm{pk}}/σ_{\rm H}$, we can obtain the probability distribution of $\bar a_*$, $P(\bar a_*)$, through the probability distribution of $ν$ characterized by a given power spectrum of the fluctuation. $P(\bar a_*)$ depends on $σ_{\rm H}$ and the parameter $γ$ that characterizes the width of the power spectrum. It is shown that, in the parameter regions of our interests, substantial values of PBH spins are expected in contrast to the PBH formation in a radiation-dominated universe.

gr-qc↗

arXiv2023

Revisiting compaction functions for primordial black hole formation

Shibata and Sasaki [arXiv:gr-qc/9905064] introduced the so-called compaction function. Since then, it has been empirically established that the maximum value of this function (or its volume-averaged counterpart) in the long-wavelength solutions gives a very robust threshold of primordial black hole formation. In this paper, we show that in spite of initial intention, the Shibata-Sasaki compaction function cannot be interpreted as the ratio of the mass excess to the areal radius in the constant-mean-curvature slice of their choice but coincides with that in the {\it comoving} slice up to a constant factor depending on the equation of state. We also discuss the gauge-(in)dependence of the legitimate compaction function, i.e., the ratio of the mass excess to the areal radius, in the long-wavelength solutions.

gr-qc↗

arXiv2023

Spins of primordial black holes formed with a soft equation of state

We investigate the probability distribution of the spins of primordial black holes (PBHs) formed in the universe dominated by a perfect fluid with the linear equation of state $p=wρ$, where $p$ and $ρ$ are the pressure and energy density of the fluid, respectively. We particularly focus on the parameter region $0<w\leq 1/3$ since the larger value of the spin is expected for the softer equation of state than that of the radiation fluid ($w=1/3$). The angular momentum inside the collapsing region is estimated based on the linear perturbation equation at the turn-around time which we define as the time when the linear velocity perturbation in the conformal Newtonian gauge takes the minimum value. The probability distribution is derived based on the peak theory with the Gaussian curvature perturbation. We find that the root mean square of the non-dimensional Kerr parameter $\sqrt{\langle a_{*}^2\rangle}$ is approximately proportional to $(M/M_{H})^{-1/3}(6w)^{-(1+2w)/(1+3w)}$, where $M$ and $M_{H}$ are the mass of the PBH and the horizon mass at the horizon entry, respectively. Therefore the typical value of the spin parameter decreases with the value of $w$. We also evaluate the mass and spin distribution $P(a_{*}, M)$, taking account of the critical phenomena. We find that, while the spin is mostly distributed in the range of $10^{-3.9}\leq a_{*}\leq 10^{-1.8}$ for the radiation-dominated universe, the peak of the spin distribution is shifted to the larger range $10^{-3.0}\leq a_{*}\leq 10^{-0.7}$ for $w=10^{-3}$.

gr-qc↗

arXiv2022

Effective inspiral spin distribution of primordial black hole binaries

We investigate the probability distribution of the effective inspiral spin, the mass ratio, and the chirp mass of primordial black hole (PBH) binaries, incorporating the effect of the critical phenomena of gravitational collapse. As a leading order estimation, each binary is assumed to be formed from two PBHs that are randomly chosen according to the probability distribution of single PBHs. We find that, although the critical phenomena can lead to large spins on the low-mass tail, the effective inspiral spin of the binary is statistically very small, $\sqrt{\langleχ_{\mathrm{eff}}^2\rangle}=8.41\times10^{-4}$. We also see that there is almost no anti-correlation between the effective inspiral spin and the mass ratio, which can be inferred from observations.

gr-qc↗

arXiv2022

Dynamical photon sphere and time evolving shadow around black holes with temporal accretion

A photon sphere is known as the geometrical structure shaping a black hole shadow. The mechanism is well understood for static or stationary black hole spacetimes such as the Schwarzschild and the Kerr spacetimes. In this paper, we investigate and explicitly specify a photon sphere that shapes a black hole shadow in a dynamical spacetime while taking the global structure of the spacetime into account. We consider dynamical and eternal black hole cases of the Vaidya spacetime, which represents a spherically symmetric black hole with accreting null dust. First, we numerically show that there are the dynamical photon sphere and photon orbits corresponding to the shadow edge in a moderate accretion case. Second, the photon spheres are derived analytically in special cases. Finally, we discuss the relation between our photon sphere and the several notions defined as a photon sphere generalization.

gr-qc↗

arXiv2021

Photon surfaces in less symmetric spacetimes

We investigate photon surfaces and their stability in a less symmetric spacetime, a general static warped product with a warping function acting on a Riemannian submanifold of codimension two. We find a one-dimensional pseudopotential that gives photon surfaces as its extrema regardless of the spatial symmetry of the submanifold. The maxima and minima correspond to unstable and stable photon surfaces, respectively. It is analogous to the potential giving null circular orbits in a spherically symmetric spacetime. We also see that photon surfaces indeed exist for the spacetimes which are solutions to the Einstein equation. The parameter values for which the photon surfaces exist are specified. As we show finally, the pseudopotential arises due to the separability of the null geodesic equation, and the separability comes from the existence of a Killing tensor in the spacetime. The result leads to the conclusion that photon surfaces may exist even in a less symmetric spacetime if the spacetime admits a Killing tensor.

gr-qc↗

arXiv2021

Spins of primordial black holes formed in the radiation-dominated phase of the universe: first-order effect

The standard deviation of the initial values of the nondimensional Kerr parameter $a_{*}$ of primordial black holes (PBHs) formed in the radiation-dominated phase of the universe is estimated to the first order of perturbation for the narrow power spectrum. Evaluating the angular momentum at turn around based on linearly extrapolated transfer functions and peak theory, we obtain the expression $\sqrt{\langle a_{*}^{2} \rangle} \simeq 4.0\times 10^{-3} (M/M_{H})^{-1/3}\sqrt{1-γ^{2}}[1-0.072 \log_{10}(β_{0}(M_{H})/(1.3\times 10^{-15}))]^{-1}$, where $M_{H}$, $β_{0}(M_{H})$, and $γ$ are the mass within the Hubble horizon at the horizon entry of the overdense region, the fraction of the universe which collapsed to PBHs at the scale of $M_{H}$, and a quantity which characterizes the width of the power spectrum, respectively. This implies that for $M\simeq M_{H}$, the higher the probability of the PBH formation, the larger the standard deviation of the spins, while PBHs of $M\ll M_{H}$ formed through near-critical collapse may have larger spins than those of $M\simeq M_{H}$. In comparison to the previous estimate, the new estimate has the explicit dependence on the ratio $M/M_{\rm H}$ and no direct dependence on the current dark matter density. On the other hand, it suggests that the first-order effect can be numerically comparable to the second-order one.

astro-ph.CO↗