An upper bound on the minimum orbital period of black holes

Abstract

Previous research has focused on establishing lower bounds on the minimum orbital period of black holes. In this work, we explore the complementary question of whether an upper bound exists for the minimum orbital period of black holes. We investigate the minimum orbital periods of three types of black holes: Schwarzschild, Reissner-Nordström and Kerr-Newman black holes. We find that the minimum orbital period of these black holes is bounded by an upper limit $T_{min}⩽6\sqrt{3}\pi M$, where $M$ is the black hole mass. Our results suggest that this upper bound on the minimum orbital period may be a general property in black hole spacetimes.

This preprint has been merged with arXiv:2505.23000, which has been updated to the unified work "Bounds on the minimum orbital period of four-dimensional black holes: From singular to non-singular spacetimes." The updated version contains all results of this preprint and supersedes it, so this preprint is withdrawn to avoid duplication