Lower bound on the orbital period of Kerr-Newman black holes

Abstract

Based on the orbital period of Kerr black holes, Hod proposed a conjecture that a general lower bound on the orbital period may exist. In this work, we examined this bound by exploring the orbital period of Kerr-Newman black holes using analytical and numerical methods. By choosing different charge and spin of Kerr-Newman black holes, we found a lower bound for the orbital period of Kerr-Newman black holes as $T(r)\geqslant 4\pi M$, where $r$ is the orbital radius, $T(r)$ is the orbital period observed from infinity and $M$ is the black hole mass. This bound is just the same as Hod's conjectured lower bound. So our results further demonstrated that Hod's lower bound may be a general property in black hole spacetimes.