The geometry of photon surfaces

By Clarissa-Marie Claudel, G. Ellis. 2000

568 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/5fe8c5db0c8fd9d5570ceb8e6d3a18e6f0e08cb7

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Citations in the corpus

Applications of the Gauss–Bonnet theorem to gravitational lensing (2008, background): “The existence of photon spheres for static, spherically symmetric metrics was first discussed in [10], and more generally, in terms of an energy condition, in [11].”
Shadows and deflection angle of charged and slowly rotating black holes in Einstein-Æther theory (2019, background): “mk Theoretically, the shadow cast by the black hole horizon is studied as null geodesics and the existence of a photon sphere or photon region (see [6] and references therein for discussions about the geometric properties of photon sphere.”
A volume preserving flow and the isoperimetric problem in warped product spaces (2016, methodology): “A totally umbilical timelike hypersurface T of a spacetime S is called a photon sphere [4], where null geodesics are trapped (i.”
Born–Infeld inspired modifications of gravity (2017, methodology): “This approach is based on the concept of strong singularities, originally introduced by Ellis and Schmidt [152].”
Gravitational Lensing in Presence of Plasma: Strong Lens Systems, Black Hole Lensing and Shadow (2017, background): “itational lensing beyond weak deﬂection approximation becomes very popular, because in the strong ﬁeld regime it is possible to diﬀer and compare diﬀerent theories of gravity, see, for example, Refs. [57, 3, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78]. Nevertheless, there are no ”
Black-bounce to traversable wormhole (2018, background): “Let us now find the location of both the photon sphere for massless particles [63–68] and the ISCO for massive particles as functions of m and a.”
Lagrangian Coherent Structures (2015, background): “As null geodesics of a Lorentzian metric that have periodic space-like projections, limit cycles of η±λ are mathematically equivalent to photon spheres (Claudel et al. 2001) surrounding black holes in general relativity.”