Light rings of stationary spacetimes

TL;DR

This paper proves that stationary, axisymmetric spacetimes with ergoregions necessarily contain at least one light ring outside the ergoregion, extending to certain black hole solutions.

Contribution

It introduces a new theorem establishing the existence of light rings outside ergoregions in stationary spacetimes, with potential extensions to specific black hole geometries.

Findings

Any stationary, axisymmetric, asymptotically flat spacetime with an ergoregion has at least one light ring outside it.

Discussion of possible extensions to asymptotically de-Sitter and anti-de-Sitter black holes.

The theorem applies to 1+3 dimensional spacetimes with ergoregions.

Abstract

We present a novel theorem regarding light rings in a stationary spacetime with an ergoregion. We prove that any stationary, axisymmetric, and asymptotically flat spacetime in 1 + 3 dimensions with an ergoregion must have at least one light ring outside the ergoregion. A possible extension of the proof for asymptotically de-Sitter and anti-de-Sitter spherically symmetric black holes is also discussed.