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The geometry of photon surfaces. (English) Zbl 1061.83525

Summary: 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 \(\text{SO}(3)\times\mathbb R\)-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 \(\text{SO}(3)\)-invariant photon surface in a general nonstatic spherically symmetric space-time. Many examples are provided.

MSC:

83C75 Space-time singularities, cosmic censorship, etc.
83C50 Electromagnetic fields in general relativity and gravitational theory
83C57 Black holes
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