Photon surface
Photon sphere ("definition"): A photon sphere of a static spherically symmetric metric is a timelike hypersurface formula_1 if the deflection angle of a light ray with the closest distance of approach formula_2 diverges as formula_3 For a general static spherically symmetric metric formula_4 the photon sphere equation is: formula_5 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∈"T"S, there exists a null geodesic formula_6:(-ε,ε)→M of (M,g) such that formula_7(0)=k, |γ|⊂S. Both definitions give the same result for a general static spherically symmetric metric. Theorem: 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.