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Photon sphere (definition[1][2]):
A photon sphere of a static spherically symmetric metric is a timelike hypersurface if the deflection angle of a light ray with the closest distance of approach diverges as
![]() | This article may be too technical for most readers to understand. (July 2011) |
For a general static spherically symmetric metric
the photon sphere equation is:
The concept of a photon sphere in a static spherically metric was generalized to a photon surface of any metric.
Photon surface (definition[3]) :
A photon surface of (M,g) is an immersed, nowhere spacelike hypersurface S of (M, g) such that, for every point p∈S and every null vector k∈TpS, there exists a null geodesic :(-ε,ε)→M of (M,g) such that (0)=k, |γ|⊂S.
Both definitions give the same result for a general static spherically symmetric metric.[3]
Theorem:[3]
Subject to an energy condition, a black hole in any spherically symmetric spacetime must be surrounded by a photon sphere. Conversely, subject to an energy condition, any photon sphere must cover more than a certain amount of matter, a black hole, or a naked singularity.