Photon sphere uniqueness in higher-dimensional electrovacuum spacetimes

TL;DR

This paper proves a uniqueness theorem for higher-dimensional Reissner-Nordström spacetimes with photon spheres, extending previous results and employing advanced geometric techniques in the context of static, electrovacuum, asymptotically flat manifolds.

Contribution

It establishes a new uniqueness result for higher-dimensional Reissner-Nordström manifolds with photon spheres under specific conditions, generalizing earlier theorems.

Findings

Uniqueness of higher-dimensional Reissner-Nordström manifolds with photon spheres.

Extension of previous Schwarzschild and Reissner-Nordström uniqueness results.

Application of modern geometric techniques to prove the theorem.

Abstract

We show a uniqueness result for the n-dimensional spatial Reissner-Nordstr\"om manifold: a static, electrovacuum, asymptotically flat system which is asymptotically Reissner-Nordstr\"om is a subextremal Reissner-Nordstr\"om manifold with positive mass, provided that its inner boundary is a (possibly disconnected) photon sphere that fulfils a suitably defined quasilocal subextremality condition. Our result implies a number of earlier uniqueness results for the Schwarzschild and the Reissner-Nordstr\"om manifolds in the static, (electro-)vacuum, asymptotically flat context, both for photon sphere and black hole inner boundaries, in the tradition of Bunting-Masood-ul Alaam [1] and Ruback [16]. The proof relies on the ideas from those works, combined with newer techniques developed by Cederbaum-Galloway [6] and Cederbaum [2].