Cunha Pedro V P, Herdeiro Carlos A R
Max Planck Institute for Gravitational Physics-Albert Einstein Institute, Am Mühlenberg 1, Potsdam 14476, Germany.
Departamento de Matemática da Universidade de Aveiro and CIDMA, Campus de Santiago, 3810-183 Aveiro, Portugal.
Phys Rev Lett. 2020 May 8;124(18):181101. doi: 10.1103/PhysRevLett.124.181101.
The ringdown and shadow of the astrophysically significant Kerr black hole (BH) are both intimately connected to a special set of bound null orbits known as light rings (LRs). Does it hold that a generic equilibrium BH must possess such orbits? In this Letter we prove the following theorem. A stationary, axisymmetric, asymptotically flat black hole spacetime in 1+3 dimensions, with a nonextremal, topologically spherical, Killing horizon admits, at least, one standard LR outside the horizon for each rotation sense. The proof relies on a topological argument and assumes C^{2} smoothness and circularity, but makes no use of the field equations. The argument is also adapted to recover a previous theorem establishing that a horizonless ultracompact object must admit an even number of nondegenerate LRs, one of which is stable.
具有天体物理学意义的克尔黑洞（BH）的铃宕和阴影都与一组特殊的束缚零轨道密切相关，这些轨道被称为光环（LRs）。一般的平衡黑洞是否一定拥有这样的轨道呢？在本快报中，我们证明了以下定理。在1 + 3维中，一个静止、轴对称、渐近平坦的黑洞时空，具有非极端、拓扑球形的 Killing 视界，对于每种旋转方向，在视界之外至少允许一个标准光环。证明依赖于一个拓扑论证，并假设(C^{2})光滑性和圆度，但不使用场方程。该论证还适用于恢复之前的一个定理，该定理表明一个无视界的超紧致物体必须允许偶数个非退化光环，其中一个是稳定的。
