Photons carry momenta, momentum is conserved in closed systems, so what would happen when a photon enters a black hole? Supposedly the momentum of the photon will be transferred to the new combined body of black hole and photon (i.e. a more massive black hole), but when is this transferring going to take place? At the photon's entry into the event horizon? Never? Or perhaps the acceleration process last until the end of the universe? Or is there some error in the whole premise?
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The combined black hole-photon system will have conserved momentum at all times, even if the photon is a billion light years away. Your question effectively seems to be 'when does a photon merge with a black hole?' which is a separate topic... – lemon May 10 '17 at 07:27
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Would the velocity of the blackhole change at all before and after the photon enter its event horizon? – user289661 May 15 '17 at 13:43
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If the photon crosses the event horizon then yes, the momentum of the black hole will change. You may ask 'but precisely when will this change occur?' and that comes down to whenever the definition of 'black hole' includes the photon... – lemon May 15 '17 at 14:34
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Related: https://physics.stackexchange.com/q/360930/2451 – Qmechanic Jan 19 '20 at 12:43