An Etymological Dictionary of Astronomy and Astrophysics

A surface where if a photon is emitted from one of its points the photon follows a closed orbit and returns periodically to its departure point. Such a surface exists only near sufficiently → compact objects where the → curvature of → space-time is very important. In other words, a body can take a stable orbit around a → black hole provided that it moves with the → speed of light.
However, only photons can have such a velocity; hence the term “photon sphere.” For a non-rotating → Schwarzschild black hole, the photon sphere has a radius of R = 3GM/c² = 3 R_S/2, where G is the → gravitational constant, M is the mass, c is the → speed of light, and R_S is the → Schwarzschild radius.
For a rotating, → Kerr black hole, the situation is much more
complex due to the → Lense-Thirring effect. In that case circular paths exist for radii whose values depend on the rotation direction. More specifically, in the equatorial plane there are two possible circular light paths: a smaller one in the direction of the rotation, and a larger one in the opposite direction.

See also: → photon; → sphere.