Bounds on the minimum orbital period of four-dimensional black holes: From singular to non-singular spacetimes

Abstract

It was conjectured that the lower bound $T_{\min }\ge 4\pi M$ may be a universal property of four-dimensional black holes, where $M$ is the black hole mass and $T_{\min }$ is the minimum orbital period around black holes. Recently, we established an upper bound $T_{\min }\le 6\sqrt{3}\pi M$ for Schwarzschild, Reissner--Nordström and Kerr--Newman black holes [23]. In this work we incorporate that analysis, which is not intended for separate publication, into a unified treatment and extend it to the non-singular Hayward and Bardeen black holes, demonstrating that the combined bounds $4\pi M\le T_{\min }\le 6\sqrt{3}\pi M$ hold for all five types of four-dimensional black holes investigated here. For all types of studied black holes, the upper bound is saturated by the standard Schwarzschild black hole and the lower bound by the maximally rotating Kerr black hole, suggesting that these bounds $4\pi M\le T_{\min }\le 6\sqrt{3}\pi M$ may be a universal property of four-dimensional black holes with horizons.

18 pages, 4 figures. v2: merged with arXiv:2504.09061; added analytic results: monotonicity in Q (RN), upper bound in KN black hole, small-parameter expansions (Hayward, Bardeen). H. Huang, F. Yang added as co-authors; all agreed