Claudel, Clarissa-Marie; Virbhadra, K. S.; Ellis, G. F. R. The geometry of photon surfaces. (English) Zbl 1061.83525 J. Math. Phys. 42, No. 2, 818-838 (2001). 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. Cited in 91 Documents MSC: 83C75 Space-time singularities, cosmic censorship, etc. 83C50 Electromagnetic fields in general relativity and gravitational theory 83C57 Black holes PDFBibTeX XMLCite \textit{C.-M. Claudel} et al., J. Math. Phys. 42, No. 2, 818--838 (2001; Zbl 1061.83525) Full Text: DOI arXiv References: [1] Darwin, Proc. R. Soc. London A 249 pp 180– (1958) · Zbl 0085.42603 · doi:10.1098/rspa.1959.0015 [2] Darwin, Proc. R. Soc. London A 263 pp 39– (1961) [3] Virbhadra, Phys. Rev. D 62 pp 084003– (2000) [4] K. S. Virbhadra and G. F. R. Ellis, ”Gravitational lensing by naked singularities.” [5] S. W. Hawking and G. F. R. Ellis,The Large Scale Structure of Space–time(Cambridge University Press, Cambridge, 1973). · Zbl 0265.53054 [6] Carter, Phys. Rev. 141 pp 1242– (1966) [7] Boyer, Proc. R. Soc. London A 311 pp 245– (1969) [8] H. Stephani,General Relativity. An Introduction to the Theory of the Gravitational Field(Cambridge University Press, Cambridge, 1982), p. 222. [9] Janis, Phys. Rev. Lett. 20 pp 878– (1968) [10] Virbhadra, Int. J. Mod. Phys. A 12 pp 4831– (1997) [11] Virbhadra, Astron. Astrophys. 337 pp 1– (1998) [12] Horne, Phys. Rev. D 46 pp 1340– (1992) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.