Photon sphere uniqueness in higher-dimensional electrovacuum spacetimes

We show a uniqueness result for the n-dimensional spatial Reissner–Nordström manifold: a static, electrovacuum, asymptotically flat system which is asymptotically Reissner–Nordström is a subextremal Reissner–Nordström 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–Nordström 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 (1987 Gen. Relativ. Gravit. 19 147–54) and Ruback (1988 Class. Quantum Grav. 5 L155–9). The proof relies on the ideas from those works, combined with newer techniques developed by Cederbaum and Galloway (2017 Commun. Anal. Geom. 25 303–20) and Cederbaum (in progress). The author kindly made a draft available to us. (paper)