Black hole physics
Photon sphere
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 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 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.