Uniqueness of photon spheres via positive mass rigidity

TL;DR

This paper proves the uniqueness of photon spheres in static vacuum asymptotically flat spacetimes, allowing multiple photon spheres and ruling out certain static multi-body configurations involving black holes.

Contribution

It extends previous uniqueness results by adapting the Bunting and Masood-ul-Alam approach, relaxing assumptions and allowing multiple photon spheres.

Findings

Uniqueness of photon spheres established in broader settings.

Multiple photon spheres are permitted in the new framework.

Static configurations with multiple compact bodies and black holes are ruled out.

Abstract

In a recent paper the first author established the uniqueness of photon spheres, suitably defined, in static vacuum asymptotically flat spacetimes by adapting Israel's proof of static black hole uniqueness. In this note we establish uniqueness of photon spheres by adapting the argument of Bunting and Masood-ul-Alam, which then allows certain assumptions to be relaxed. In particular, multiple photon spheres are allowed a priori. As a consequence of our result, we can rule out the existence of static configurations involving multiple "very compact" bodies and black holes.