| 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 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.
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