Photon sphere uniqueness in higher-dimensional electrovacuum spacetimes

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].