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 (exterior) Schwarzschild, Reissner-Nordström, and Schwarzschild-anti de Sitter in n + 1 dimensions. In the second part, we prove that any static, vacuum, and "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 obtained by the first author.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics