Can Photons Actually Orbit Massive Objects?

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Einstein's theory of general relativity suggests that light bends around massive objects due to the curvature of space. It is theoretically possible for photons to orbit a massive body, such as a black hole, at a specific radius of r = 3GM/c2. However, this orbit is unstable, meaning photons cannot remain in this orbit indefinitely. Any photon in this unstable orbit will either be drawn into the black hole or escape to infinity. Thus, while photon orbits around massive objects can exist, they are not sustainable.
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According to Einstein's theory of general relativity, light bends--or rather space bends--around mass. So, in theory, is it possible for a photon to orbit around a body of sufficiently large mass?
 
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Well, I think that this is possible - black holes are such objects.
 
Yes, a circular photon orbit is possible at r = 3GM/c2. (The Schwarzschild radius, which defines the 'surface' of the black hole is 2GM/c2) However the orbit is unstable, meaning that photons won't accumulate there, and any photon that is placed there will eventually fall into the hole or run off to infinity.
 
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