The geometry of photon surfaces
Clarissa-Marie ClaudelMathematical Institute, University of Umeå, 901 87 Umeå, SwedenK. S. VirbhadraDepartment of Applied Mathematics, University of Cape Town, Rondebosch 7701, South AfricaG. F. R. EllisDepartment of Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa
2001en
ABI
Abstract
The photon sphere concept in Schwarzschild space–time is generalized to a definition of a photon surface in an arbitrary space–time. A photon sphere is then defined as an SO(3)×R-invariant photon surface in a static spherically symmetric space–time. It is proved, subject to an energy condition, that a black hole in any such space–time must be surrounded by a photon sphere. Conversely, subject to an energy condition, any photon sphere must surround a black hole, a naked singularity or more than a certain amount of matter. A second order evolution equation is obtained for the area of an SO(3)-invariant photon surface in a general nonstatic spherically symmetric space–time. Many examples are provided.
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