Uniqueness of photon spheres in electro-vacuum spacetimes

TL;DR

This paper proves the uniqueness of certain photon spheres in static electro-vacuum spacetimes, ruling out multiple charged bodies and black holes configurations, extending previous vacuum results.

Contribution

It extends the uniqueness proof of photon spheres to electro-vacuum spacetimes, adapting existing methods to include electric charge effects.

Findings

Uniqueness of sub-extremal photon spheres established

Multiple charged bodies and black hole configurations are ruled out

Extends vacuum spacetime results to electro-vacuum cases

Abstract

In a recent paper, the authors established the uniqueness of photon spheres in static vacuum asymptotically flat spacetimes by adapting Bunting and Masood-ul-Alam's proof of static vacuum black hole uniqueness. Here, we establish uniqueness of suitably defined sub-extremal photon spheres in static electro-vacuum asymptotically flat spacetimes by adapting the argument of Masood-ul-Alam. As a consequence of our result, we can rule out the existence of electrostatic configurations involving multiple "very compact" electrically charged bodies and sub-extremal black holes.