ペンローズによって証明された「特異点定理」によると、宇宙には必ずどこかに特異点が存在する。この特異点とは、時空の曲率が無限大になり一般相対性理論が破綻する点である。それは、例えば、ブラックホールの内部や宇宙の始まった瞬間に存在すると考えられている。このような点の近傍を記述するためには量子重力が必要だと考えられているが、現時点では未完成の理論である。将来的に量子重力理論が完成すれば、このような特異性は解消されると期待されている。量子重力理論の完成には長い年月がかかるので、量子重力のブラックホールの候補として「特異点のないブラックホール（non-singular black hole, regular black hole）」のモデルを考える研究が世界的に盛んに行われている。本研究室では、観測と整合的な「特異点のないブラックホールモデル」の性質を研究している。

成果：

2023年度
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年度
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.

ブラックホールとは、そこから何も出て来ることができない宇宙の領域のことである。ところが、この何も出てこないブラックホールの古典的描像は、量子論を考えると大きく変わる。ブラックホールは、その周りで、量子効果による粒子生成によりプランク分布に従う熱的放射（ホーキング輻射）をして最終的には蒸発するという驚きの性質を持っている。しかし、宇宙にあるブラックホールの輻射はあまりにも微弱であるため観測することは不可能だと考えられている。そのため、ホーキング輻射の観測のためブラックホールと似た振る舞いをする流体ブラックホールが近年世界中で盛んに研究されてきた。なぜなら、流体中の音の伝搬とブラックホール時空の光の伝搬はよく似ていて流体ブラックホールは実験室で作れるからである。本研究室でも、ホーキング輻射だけではなく、ブラックホールに関わる物理現象を実験室で検証することを目標に、様々なタイプの流体ブラックホールのモデルを考案している。

成果：

2023年度
We proposed a new simple model of acoustic black hole in a thin tube, where the difference in the gravitational potential is used to create a transonic flow. The main merit of our transonic flow model is that the Euler equations can be solved analytically. In fact, we obtained an exact solution to the equation in terms of a height function in the monatomic case. For a more general case, we found that it takes a simple form by the near-sonic approximation. Moreover, we obtained two analytic solutions describing a backward wave and a forward wave, from which we confirmed the existence of sonic horizons.

　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．

成果：

2023年度
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年度
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年度
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.

　この２０年余りの研究成果から、高次元ブラックホールの多様な構造が明らかになりつつある．４次元の真空な定常時空においては、ブラックホールのトポロジーは球面だけに制限され、そのようなブラックホールを記述する解は、質量と角運動量というパラメーターだけで特徴付けられる「カーブラックホール解」が唯一つの解であることが数学的に証明されている．これはブラックホールの「一意性定理」と呼ばれ、４次元の一般相対性理論の最も大きな成果の１つと言える．これとは対照的に、高次元理論では、許されるブラックホールのトポロジーは球面１つだけではない．実際に、５次元時空の漸近平坦な真空解として、同じ質量と角運動量を持つが、トポロジーの異なる２つの解、球面のブラックホール解とリング形状のブラックリング解、そしてレンズ空間のブラックレンズ解が発見されたのである[Tomizawa and Nozawa(2016)].本研究では、特にブラックレンズに着目し、ブラックホールとは異なる物理的特性を明らかすることを試みる．

成果：

2023年度
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年度
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.

　LIGOによる重力波の発見によって、現代物理学の新しい時代の扉が開かれた．特に、重力波の基礎的性質の解明はその分野の研究の基盤として重要である．本研究では、重力波のモード間あるいは電磁波‐重力波間の強い転換現象の解析を行った．今後、天体現象における重力波の発生において、電磁波‐重力波の強相関的現象も考慮されなければないため、そのような解析の礎となるだろう．さらに、ブラックホール研究で開発された方法を非線形重力波の解析に応用し、重力ファラデー効果や重力波の非線形現象の研究も行っている．

成果：

2023年度
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年度
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。

成果：

2023年度
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年度
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→∞.