Photon surfaces with equipotential time-slices

Abstract

Photon surfaces are timelike, totally umbilic hypersurfaces of Lorentzian spacetimes. In the first part of this paper, we locally characterize all possible photon surfaces in a class of static, spherically symmetric spacetimes that includes Schwarzschild, Reissner--Nordström, Schwarzschild-anti de Sitter, etc., in $n+1$ dimensions. In the second part, we prove that any static, vacuum, "asymptotically isotropic" $n+1$-dimensional spacetime that possesses what we call an "equipotential" and "outward directed" photon surface is isometric to the Schwarzschild spacetime of the same (necessarily positive) mass, using a uniqueness result by the first named author.

arXiv comment33 pages, 1 figure We have added a discussion of generating null geodesics and related topics at the end of Section 3 and have simplified some computations

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• Nondivergent deflection of light around a photon sphere of a compact object
• Some new perspectives on the Kruskal--Szekeres extension with applications to photon surfaces
• Uniqueness of photon sphere for Reissner-Nordström electric-magnetic system
• 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 equipotential photon surfaces in 4-dimensional static vacuum asymptotically flat spacetimes for positive, negative, and zero mass -- and a new partial proof of the Willmore inequality
• Uniqueness of electric-magnetic spacetimes with massive particle
• Existence of steady states of the massless Einstein-Vlasov system surrounding a Schwarzschild black hole