The geometry of photon surfaces
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)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.
Keywords
Cite
@article{arxiv.gr-qc/0005050,
title = {The geometry of photon surfaces},
author = {Clarissa-Marie Claudel and K. S. Virbhadra and G. F. R. Ellis},
journal= {arXiv preprint arXiv:gr-qc/0005050},
year = {2010}
}
Comments
24 pages, 5 figures. Uses the following packages: amsmath, amsthm, amssymb, amsfonts, mathrsfs, enumerate, graphicx