arXiv subjects

Takahisa Igata

Publications and source records attributed to Takahisa Igata.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2020

Stable bound orbits in black lens backgrounds

In contrast to five-dimensional Schwarzschild-Tangherlini and Myers-Perry backgrounds, we show that there are stable bound orbits of massive/massless particles in five-dimensional black lens backgrounds, in particular, the supersymmetric black lens with $L(2,1)$ and $L(3,1)$ topologies. We also show that in the zero-energy limit of massless particles, there exist stable circular orbits on the evanescent ergosurfaces.

hep-th↗

arXiv2020

Stable circular orbits in higher-dimensional multi-black hole spacetimes

We consider the dynamics of particles, particularly focusing on circular orbits in the higher-dimensional Majumdar-Papapetrou (MP) spacetimes with two equal mass black holes. It is widely known that in the 5D Schwarzschild-Tangherlini and Myers-Perry backgrounds, there are no stable circular orbits. In contrast, we show that in the 5D MP background, stable circular orbits can always exist when the separation of two black holes is large enough. More precisely, for a large separation, stable circular orbits exist from the vicinity of horizons to infinity; for a medium one, they appear only in a certain finite region bounded by the innermost stable circular orbit and the outermost stable circular orbit outside the horizons; for a small one, they do not appear at all. Moreover, we show that in MP spacetimes in more than 5D, they do not exist for any separations.

hep-th↗

arXiv2020

Chaotic particle motion around a homogeneous circular ring

We consider test particle motion in a gravitational field generated by a homogeneous circular ring placed in $n$-dimensional Euclidean space. We observe that there exist no stable stationary orbits in $n=6, 7, \ldots, 10$ but exist in $n=3, 4, 5$ and clarify the regions in which they appear. In $n=3$, we show that the separation of variables of the Hamilton-Jacobi equation does not occur though we find no signs of chaos for stable bound orbits. Since the system is integrable in $n=4$, no chaos appears. In $n=5$, we find some chaotic stable bound orbits. Therefore, this system is nonintegrable at least in $n=5$ and suggests that the timelike geodesic system in the corresponding black ring spacetimes is nonintegrable.

gr-qc↗

arXiv2020

Particle dynamics in the Newtonian potential sourced by a homogeneous circular ring

Newtonian gravitational potential sourced by a homogeneous circular ring in arbitrary dimensional Euclidean space takes a simple form if the spatial dimension is even. In contrast, if the spatial dimension is odd, it is given in a form that includes complete elliptic integrals. In this paper, we analyze the dynamics of a freely falling massive particle in its Newtonian potential. Focusing on circular orbits on the symmetric plane where the ring is placed, we observe that they are unstable in 4D space and above, while they are stable in 3D space. The sequence of stable circular orbits disappears at $1.6095\cdots$ times the radius of the ring, which corresponds to the innermost stable circular orbit (ISCO). On the axis of symmetry of the ring, there are no circular orbits in 3D space but more than in 4D space. In particular, the circular orbits are stable between the ISCO and infinity in 4D space and between the ISCO and the outermost stable circular orbit in 5D space. There exist no stable circular orbits in 6D space and above.

gr-qc↗

arXiv2020

Observability of the innermost stable circular orbit in a near-extremal Kerr black hole

We consider the escape probability of a photon emitted from the innermost stable circular orbit (ISCO) of a rapidly rotating black hole. As an isotropically emitting light source on a circular orbit reduces its orbital radius, the escape probability of a photon emitted from it decreases monotonically. The escape probability evaluated at the ISCO also decreases monotonically as the black hole spin increases. When the dimensionless Kerr parameter $a$ is at the Thorne limit $a=0.998$, the escape probability from the ISCO is $58.8\%$. In the extremal case $a=1$, even if the orbital radius of the light source is arbitrarily close to the ISCO radius, which coincides with the horizon radius, the escape probability remains at $54.6\%$. We also show that such photons that have escaped from the vicinity of the horizon reach infinity with sufficient energy to be potentially observed because Doppler blueshift due to relativistic beaming can overcome the gravitational redshift. Our findings indicate that signs of the near-horizon physics of a rapidly rotating black hole will be detectable on the edge of its shadow.

astro-ph.HE↗

arXiv2019

Effect of a second compact object on stable circular orbits

We investigate how stable circular orbits around a main compact object appear depending on the presence of a second one by using the Majumudar--Papapetrou dihole spacetime, which consists of the two extremal Reissner--Nordstr\" om black holes with different masses. While the parameter range of the separation of the two objects is divided due to the appearance of stable circular orbits, this division depends on its mass ratio. We show that the mass ratio range separates into four parts, and we find three critical values as the boundaries.

gr-qc↗

arXiv2019

Escape probability of a photon emitted near the black hole horizon

We investigate the escape of photons from the vicinity of the horizon to infinity in the Kerr-Newmann black hole spacetime. We assume that a light source is at rest in a locally nonrotating frame and photons are emitted isotropically. Then, we evaluate the escape probability of the emitted photons. The main result of this paper is the following. If the black hole is extremal with the nondimensional spin parameter $a_*> 1/2$, however close to the horizon the light source would be, the escape probability remains nonzero. The near-horizon limit value of the escape probability is a monotonically increasing function of $a_*$ and takes a maximum $\sim$29.1\% at $a_*=1$, i.e., for the extremal Kerr case. On the other hand, if the black hole is extremal with $0\leq a_*\leq 1/2$ or if the black hole is subextremal, the near-horizon limit value is zero.

gr-qc↗

arXiv2019

Observability of spherical photon orbits in near-extremal Kerr black holes

We investigate the spherical photon orbits in near-extremal Kerr spacetimes. We show that the spherical photon orbits with impact parameters in a finite range converge on the event horizon. Furthermore, we demonstrate that the Weyl curvature near the horizon does not generate the shear of a congruence of such light rays. Because of this property, a series of images produced by the light orbiting around a near-extremal Kerr black hole several times can be observable.

gr-qc↗

arXiv2019

Stable bound orbits around a supersymmetric black lens

In higher-dimensional Schwarzschild black hole spacetimes, there are no stable bound orbits of particles. In contrast to this, it is shown that there are stable bound orbits in a five-dimensional black lens spacetime.

hep-th↗

arXiv2019

Innermost stable circular orbits in Majumdar--Papapetrou dihole spacetime

We investigate the positions of stable circular massive particle orbits in the Majumdar--Papapetrou dihole spacetime with equal mass. In terms of qualitative differences of their sequences, we classify the dihole separation into five ranges and find four critical values as the boundaries. When the separation is relatively large, the sequence on the symmetric plane bifurcates, and furthermore, they extend to each innermost stable circular orbit in the vicinity of each black hole. In a certain separation range, the sequence on the symmetric plane separates into two parts. On the basis of this phenomenon, we discuss the formation of double accretion disks with a common center. Finally, we clarify the dependence of the radii of marginally stable circular orbits and innermost stable circular orbits on the separation parameter. We find a discontinuous transition of the innermost stable circular orbit radius. We also find the separation range at which the radius of the innermost stable circular orbit can be smaller than that of the stable circular photon orbit.

gr-qc↗

arXiv2019

Massive tensor field perturbations on extremal and near-extremal static black holes

We develop a new perturbation method to study the dynamics of massive tensor fields on extremal and near-extremal static black hole spacetimes in arbitrary dimensions. On such backgrounds, one can classify the components of massive tensor fields into the tensor, vector, and scalar-type components. For the tensor-type components, which arise only in higher dimensions, the massive tensor field equation reduces to a single master equation, whereas the vector and scalar-type components remain coupled. We consider the near-horizon expansion of both the geometry and the field variables with respect to the near-horizon scaling parameter. By doing so, we reduce, at each order of the expansion, the equations of motion for the vector and scalar-type components to a set of five mutually decoupled wave equations with source terms consisting only of the lower-order variables. Thus, together with the tensor-type master equation, we obtain the set of mutually decoupled equations at each order of the expansion that govern all dynamical degrees of freedom of the massive tensor field on the extremal and near-extremal static black hole background.

gr-qc↗

arXiv2018

Rigidly Rotating String Sticking in a Kerr Black Hole

We analyze rigidly rotating Nambu--Goto strings in the Kerr spacetime, particularly focusing on the strings sticking in the horizon. From the regularity on the horizon, we find the condition for sticking in the horizon, which is consistent with the second law of the black hole thermodynamics. Energy extraction through the sticking string from a Kerr black hole occurs. We obtain the maximum value of the luminosity of the energy extraction.

gr-qc↗

arXiv2018

Scale invariance and constants of motion

Scale invariance in the theory of classical mechanics can be induced from the scale invariance of background fields. In this paper we consider the relation between the scale invariance and the constants of particle motion in a self-similar spacetime, only in which the symmetry is well-defined and is generated by a homothetic vector. Relaxing the usual conservation condition by the Hamiltonian constraint in a particle system, we obtain a conservation law holding only on the constraint surface in the phase space. By the conservation law, we characterize constants of motion associated with the scale invariance not only for massless particles but for massive particles and classify the condition for the existence of the constants of motion. Furthermore, we find the explicit form of the constants of motion by solving the conservation equations.

hep-th↗

arXiv2018

Construction of test Maxwell fields with scale symmetry

Geometrical symmetry in a spacetime can generate test solutions to the Maxwell equation. We demonstrate that the source-free Maxwell equation is satisfied by any generator of spacetime self-similarity---a proper homothetic vector---identified with a vector potential of the Maxwell theory. The test fields obtained in this way share the scale symmetry of the background.

gr-qc↗

arXiv2018

Complete conformal classification of the Friedmann-Lemaitre-Robertson-Walker solutions with a linear equation of state

We completely classify Friedmann-Lemaître-Robertson-Walker solutions with spatial curvature $K=0,\pm 1$ and equation of state $p=wρ$, according to their conformal structure, singularities and trapping horizons. We do not assume any energy conditions and allow $ρ< 0$, thereby going beyond the usual well-known solutions. For each spatial curvature, there is an initial spacelike big-bang singularity for $w>-1/3$ and $ρ>0$, while no big-bang singularity for $w<-1$ and $ρ>0$. For $K=0$ or $-1$, $-1 0$, there is an initial null big-bang singularity. For each spatial curvature, there is a final spacelike future big-rip singularity for $w<-1$ and $ρ>0$, with null geodesics being future complete for $-5/3\le w<-1$ but incomplete for $w<-5/3$. For $w=-1/3$, the expansion speed is constant. For $-1 -1/3$, the universe contracts from infinity, then bounces and expands to infinity; for $-1<w<-1/3$, it starts from a big-bang singularity and contracts to a big-crunch singularity; for $w<-1$, it expands from a regular null hypersurface and contracts to another regular null hypersurface.

gr-qc↗

arXiv2018

The essence of the Blandford-Znajek process

From a spacetime perspective, the dynamics of magnetic field lines of force-free electromagnetic fields can be rewritten into a quite similar form for the dynamics of strings, i.e., dynamics of "field sheets". Using this formalism, we explicitly show that the field sheets of stationary and axisymmetric force-free electromagnetic fields have identical intrinsic properties to the world sheets of rigidly rotating Nambu-Goto strings. Thus, we conclude that the Blandford-Znajek process is kinematically identical to an energy-extraction mechanism by the Nambu-Goto string with an effective magnetic tension.

gr-qc↗

arXiv2017

Escape probability of the super-Penrose process

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.

gr-qc↗