definition 
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 spacetime 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 nonrotating Schwarzschild black hole, the photon
sphere has a radius of R = 3GM/c2 = 3 RS/2, where G is the gravitational constant,
M is the mass, c is the speed of light, and RS is the Schwarzschild radius. For a
rotating, Kerr black hole, the situation is much more complex due to the LenseThirring
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.

