Photon sphere (definition):
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
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) :
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.
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.
- K.S. Virbhadra and G. F.R. Ellis, Schwarzschild black hole lensing, Phys. Rev. D62, 084003 (2000); K.S. Virbhadra and G. F.R. Ellis, Gravitational lensing by naked singularities, Phys. Rev. D65, 103004 (2002).
- Clarissa-Marie Claudel, K.S. Virbhadra, and G.F.R. Ellis, The geometry of photon surfaces, J. Math. Phys. 42, 818-838 (2001).
- See in .
- See in .