The fastest way to circle a black hole

TL;DR

This paper proves that null circular geodesics around black holes represent the fastest possible orbits, and conjectures a universal lower bound on orbital periods for compact objects, with implications for understanding black hole dynamics.

Contribution

It establishes null circular geodesics as the fastest orbits around black holes and proposes a universal lower bound on orbital periods for compact objects.

Findings

Null circular geodesics have the shortest orbital period around black holes.

A conjectured universal lower bound for orbital periods is $T_{ ext{infty}}\, extgreater= 4\, extpi M$.

The bound is saturated by the maximally rotating Kerr black hole.

Abstract

Black-hole spacetimes with a "photonsphere", a hypersurface on which massless particles can orbit the black hole on circular null geodesics, are studied. We prove that among all possible trajectories (both geodesic and non-geodesic) which circle the central black hole, the null circular geodesic is characterized by the {\it shortest} possible orbital period as measured by asymptotic observers. Thus, null circular geodesics provide the fastest way to circle black holes. In addition, we conjecture the existence of a universal lower bound for orbital periods around compact objects (as measured by flat-space asymptotic observers): $T_{\infty}\geq 4\pi M$, where $M$ is the mass of the central object. This bound is saturated by the null circular geodesic of the maximally rotating Kerr black hole.