Fermat's principle in black-hole spacetimes

TL;DR

This paper proves that in Kerr black hole spacetimes, the closed light rings are the fastest possible null circular paths as observed from afar, revealing a fundamental property of black-hole photon orbits.

Contribution

The paper presents a compact theorem showing that black-hole light rings are the fastest null circular geodesics, a novel insight into black-hole spacetime geometry.

Findings

Closed light rings exist in black-hole spacetimes.

Light rings are the fastest null circular geodesics as measured by distant observers.

This property is specific to spinning Kerr black holes.

Abstract

Black-hole spacetimes are known to possess closed light rings. We here present a remarkably compact theorem which reveals the physically intriguing fact that these unique null circular geodesics provide the {\it fastest} way, as measured by asymptotic observers, to circle around spinning Kerr black holes.