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arXiv · 1910.04220

Photon surfaces with equipotential time-slices

Carla Cederbaum·Gregory J. Galloway
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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--Nordstr\"om, 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.

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Carla Cederbaum, Gregory J. Galloway. 2019-10-09. Photon surfaces with equipotential time-slices. https://doi.org/10.1063/5.0031280

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