Extremal black holes have external light rings

TL;DR

This paper proves that extremal black holes with spherical symmetry necessarily have at least one external light ring, using a proof based on the dominant energy condition.

Contribution

It provides a concise proof establishing the existence of external light rings in spherically symmetric extremal black holes under the dominant energy condition.

Findings

Extremal black holes have at least one external light ring.

The proof relies on the dominant energy condition.

The result applies to non-vacuum extremal black-hole spacetimes.

Abstract

It is proved that spherically symmetric extermal black holes possess at least one external light ring. Our remarkably compact proof is based on the dominant energy condition which characterizes the external matter fields in the non-vacuum extremal black-hole spacetimes.