Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-05-15
J.Math.Phys.42:818-838,2001
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
24 pages, 5 figures. Uses the following packages: amsmath, amsthm, amssymb, amsfonts, mathrsfs, enumerate, graphicx
Scientific paper
10.1063/1.1308507
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)xR-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 non-static spherically symmetric space-time. Many examples are provided.
Claudel Clarissa-Marie
Ellis George F. R.
Virbhadra K. S.
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