Outcome：

2023
General relativity coupled to nonlinear electrodynamics is known to have nonsingular black hole solutions. We have investigated the existence conditions for such solutions in two-parameter Lagrangian L(F,G). In particular, we have obtained a criterion on the Lagrangian for the existence of nonsingular black hole with a dyonic charge. In addition, we have presented a simple example of two-parameter Lagrangian satisfying the criterion, in which the existence of the dyonic solution is actually confirmed. Moreover, apart from the actual existence of dyonic solutions, we have considered some examples for the Lagrangian satisfying such a criterion.

2022
We have investigated the bound orbits of massive/massless, neutral particles and photons moving around regular black holes of Fan and Wang. For massive particles, we have shown the existence of stable/unstable circular orbits and the charge dependence of the radius of the innermost stable circular orbit. Remarkably, we found an unstable circular orbit of photons inside the event horizon. For massless particles and photons, we have shown that both stable and unstable circular orbits can exist in a regular and horizonless spacetime with a slight overcharge. Then, we also discussed the periapsis shift of massive neutral particles orbiting around the black hole, and showed that the charge gives a negative correction to the shift for black holes with small nonlinearity of electrodynamics.

　近年、超重力理論の解であるMicrostate geometryが、近似的にブラックホールの幾何学的構造を記述することから、ブラックホールの情報損失問題の解決という観点から世界的に注目されている.しかし、こうした解が、現実の宇宙にあるブラックホールを記述するかどうかは、現時点で不明である．これを明らかにするため、Microstate geometryの古典的な物理的性質（安定性、熱力学、光や粒子の挙動、重力レンズ効果、重力波放射、ホーキング輻射など）について解析を行っている．

Outcome：

2023
Using the exact solution that describes multi-centered rotating black holes, recently discovered by Teo and Wan, we have investigated the innermost stable circular orbit (ISCO) for massive particles and the circular orbit for massless particles moving around a spinning black hole binary. We assume equal masses M1 = M2 = m and equal spin angular momenta |J1| = |J2| for both black holes. Firstly, we have examined the case where two black holes are spinning in the same direction (J1 = J2). We have clarified that that for particles rotating in the same direction as (opposite directions to) black holes’ spin, the greater the spin angular momenta of the black holes, the more the radii of the ISCO for massive particles and the circular orbit for massless particles decrease (increase). We have shown that distinct ISCO transitions occur for particles rotating in the same direction as the black holes in three ranges of spin angular momenta: 0 < J1/m^2 = J2/m^2 < 0.395..., 0.395... < J1/m^2 = J2/m^2 < 0.483..., and 0.483 . . . < J1/m^2 = J2/m^2 < 0.5. Conversely, particles rotating in the opposite direction to the black holes exhibit a consistent transition pattern for the case 0 < J1/m^2 = J2/m^2 < 0.5. Secondly, we study the situation where binary black holes are spinning in opposite directions (J1 = −J2). We have clarified that for large (small) separations between black holes, the ISCO appears near the black hole that is spinning in the same (opposite) direction as particles’ rotation. Additionally, we have shown that different ISCO transitions occur in the three angular momentum ranges: 0 < J1/m^2 = −J2/m^2 < 0.160..., 0.160... < J1/m^2 = −J2/m^2 < 0.467..., and 0.467... < J1/m^2 = −J2/m^2 < 0.5.

2023
Recently, various types of the regular black hole model are reintroduced as the solution of the Einstein equations coupled with nonlinear electrodynamics (NED). In NED, it is known that photons do not propagate along the null geodesics of the spacetime geometry, but of so-called effective geometry, which suggests the possibility of so-called “faster/slower than light” photons. We have studied the relation between the causality of photons and the dominant energy condition (DEC) in some static and spherically symmetric black hole spacetimes in NED. We have shown that if photon trajectories with a nonzero angular momentum are timelike in the spacetime geometry, DEC is always satisfied in static and spherically symmetric spacetimes in any NED that admits the Maxwell limit, and vice versa, at least, in the weak field limit. Thus, this implies that in such NED, the violation of DEC admits the existence of faster than light photons.

2022
We showed the existence of stable bound orbits for the massive and massless particles moving in the simplest microstate geometry spacetime in the bosonic sector of the five-dimensional minimal supergravity. In our analysis, reducing the motion of particles to a two-dimensional potential problem, we numerically investigated whether the potential has a negative local minimum.

Outcome：

2023
We have presented the first non-BPS exact solution of an asymptotically flat, stationary spherical black hole having domain of outer communication with nontrivial topology in five-dimensional minimal supergravity. It describes a charged rotating black hole capped by a disc-shaped bubble. The existence of the ``capped black hole'' shows the non-uniqueness of spherical black holes.

2022
Applying the inverse scattering method to static and bi-axisymmetric Einstein equations, we constructed a non-rotating black lens inside a bubble of nothing whose horizon is topologically lens space of L(n;1). Using this solution, we discussed whether a static black lens can be in equilibrium by the force balance between the expansion and gravitational attraction.

Outcome：

2023
Using the ``composite harmonic mapping method," we haveconstructed exact solutions for cylindrically symmetric gravitational and electromagnetic waves within the Einstein-Maxwell system, focusing on the conversion dynamics between these types of waves. In this approach, we have employed two types of geodesic surfaces in H^2_c : (a) the complex line and (b) the totally real Lagrangian plane, applied to two different vacuum seed solutions: (i) a vacuum solution previously utilized in our studies and (ii) the solitonic vacuum solution constructed previously by Economou and Tsoubelis. We have studied three scenarios: case (a) with seeds (i) and (ii), and case (b) with seed (ii). In all cases (a) and (b), solutions demonstrate notable mode conversions near the symmetric axis. In case (a) with seed (i) or seed (ii), we have shown that any change in the occupancy of the gravitational or electromagnetic mode relative to the C-energy near the axis always reverts to its initial state once the wave moves away from the axis. Particularly in case (b) with seed (ii), nontrivial conversions occur even when the wave moves away from the axis. In this case, the amplification factors of electromagnetic modes range from an upper limit of approximately 2.4 to a lower limit of about  0.4, when comparing the contributions of electromagnetic mode to C-energy at past and future null infinities.

2022
Applying a simple harmonic map method to the cylindrically symmetric Einstein-Maxwell system, we obtained exact solutions representing strong nonlinear interaction between gravitational waves and electromagnetic waves in the case without any background field. As an interesting fact, we showed that with adjusted parameters the solution represents occurrences of large conversion phenomena in the intense region of fields near the cylindrically symmetric axis.

　Einsteinの一般相対性理論を拡張したEinstein-Gauss-Bonnet理論におけるブラックホール解を高次元極限法を用いて、理論的に解析する。特にこれまで解析が数値解や摂動解などに限られていた回転ブラックホール解の1/D展開を用いた解析解の導出および安定性解析などを行う。

Outcome：

2023
We have investigated the nonlinear dynamics of D=2N+3 Myers-Perry black holes with almost equal angular momenta, which have N equal spins out of possible N+1 spins. In particular, we have studied the ultraspinning instability and the fate of its nonlinear evolution using the large D effective theory approach. We have found that every stationary phase can be mapped to the counterpart in the singly rotating phase within the leading order effective theory. From the known results of singly rotating solutions, we have obtained the phase diagram of almost equally rotating black holes. We have also obtained a certain implication for the possible topology changing transition.

2022
The phase and stability of black strings in the Einstein-Gauss-Bonnet (EGB) theory are investigated by using the large D effective theory approach. The spacetime metric and thermodynamics are derived up to the next-to-leading order (NLO) in the 1/D expansion. We found that the entropy current defined by the Iyer-Wald formula follows the second law. As in the Einstein theory, the entropy difference from the total mass produces an entropy functional for the effective theory. Including the NLO correction, we found that for the large Gauss-Bonnet coupling constant, the Gregory-Laflamme instability of uniform black strings needs longer wavelength. Moreover, we showed that the critical dimension, beyond which non-uiform black strings becomes more stable than uniform ones, increases as α becomes large, and approaches to a finite value for α→∞.