Photon sphere uniqueness in higher-dimensional electrovacuum spacetimes

Abstract

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 [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].

References in corpus (6)

• The geometry of photon surfaces
• Towards a classification of static electro-vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior
• Uniqueness of photon spheres in electro-vacuum spacetimes
• On the positive mass theorem for manifolds with corners
• Uniqueness of the static Einstein-Maxwell spacetimes with a photon sphere
• No static bubbling spacetimes in higher dimensional Einstein-Maxwell theory

Cited by in corpus (9)

• Photon surfaces with equipotential time-slices
• Classification of static asymptotically flat spacetimes with a photon sphere in Einstein-multiple-scalar field theory
• A spinorial proof of the rigidity of the Riemannian Schwarzschild manifold
• Uniqueness of photon sphere for Reissner-Nordström electric-magnetic system
• On the geometry of electrovacuum spaces in higher dimensions
• Static Einstein-Maxwell space-time invariant by translation
• Black Hole and Equipotential Photon Surface Uniqueness in 4-dimensional Asymptotically Flat Electrostatic Electro-Vacuum Spacetimes
• Higher-dimensional electric-magnetic photon sphere uniqueness
• Uniqueness of electric-magnetic spacetimes with massive particle