Thought Exp: Light Trapped in Gravity Well of Black Hole

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ccrook
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I am not a physicist but I was curious if there was any information on the following thought experiment. Say a beam of light emitted from a far away star passed a black hole at just the right direction that it became entrapped in a sort of orbit like the moon around the earth. Is this possible and would it then be entrapped until the black hole either became more or less massive changing its pull and disrupting uniform circular motion? Or are there other effects that prevent this? Thanks in advance!
 
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I believe that such an orbit, if the light could even get into it, is extremely unstable. The slightest perturbation would disrupt it and since there are always other light rays and particles passing nearby, not to mention the gravitational influences from uncountable stars and galaxies, it wouldn't last.
 
ccrook said:
Say a beam of light emitted from a far away ... would it then be entrapped
Think of the reverse direction