Universal Properties of Light Rings for Stationary Axisymmetric Spacetimes

TL;DR

This paper explores the universal characteristics of light rings in stationary, axisymmetric spacetimes, revealing their existence, stability properties, and pairing behavior, applicable across various gravity theories.

Contribution

It provides a general, straightforward proof of light ring properties in stationary axisymmetric spacetimes, including black holes and horizonless objects, extending previous results with stronger conclusions.

Findings

Nonextremal black holes have at least two light rings with the outer one unstable.

Extremal black holes have at least one retrograde light ring.

Light rings always appear in pairs in horizonless spacetimes.

Abstract

Light rings (LRs) play an important role in gravitational wave observations and black hole photographs. In this paper, we investigate general features of LRs in stationary, axisymmetric, asymptotically flat spacetimes with or without horizons. For a nonextremal black hole, we show explicitly that there always exist at least two LRs propagating in opposite directions, where the outermost one is radially unstable. For an extremal black hole, we show that there exists at least one retrograde LR. We find that there is at least one LR which is angularly stable. The stability analysis does not involve any energy condition. Our method also applies to horizonless spacetimes and we prove that LRs always appear in pairs. Only some natural and generic assumptions are used in our proof. The results are applicable to general relativity as well as most modified theories of gravity. In contrast to previous works on this issue, we obtain much stronger results with a much more straightforward approach.