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So this random question popped up in my mind. As we know the photons get deflected if they pass in the vicinity of a black hole. At the event horizon(right before it), they form the photon sphere. The point where they start orbiting the black hole in circles. In fact they are travelling straight, it's just the space-time that's curved. But what happens when they cross the event horizon? Do they spiral down to singularity? (wondering what would such a space-time curvature even look like). And what about photons created inside the black-hole? Do they follow a parabolic trajectory like a ball thrown on Earth or do they just keep traveling in circles? Or are stuck in singularity for infinity and beyond? But then singularities can't exist as they have infinite density.

Most probably humans don't know much about this yet. But just a question that popped in my mind.

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  • $\begingroup$ The photon sphere isn't at the horizon, correct? $\endgroup$ Jun 17, 2020 at 23:34
  • $\begingroup$ See How To Understand the Black Hole Image from Veritasium $\endgroup$
    – mmesser314
    Jun 18, 2020 at 0:03
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    – David Z
    Jun 18, 2020 at 3:04
  • $\begingroup$ Comments are not for extended discussion; the remainder of this conversation has been moved to chat. $\endgroup$
    – David Z
    Jun 18, 2020 at 18:48
  • $\begingroup$ This question was answered at physics.stackexchange.com/questions/565114/… $\endgroup$
    – Yukterez
    Oct 6, 2023 at 13:38

2 Answers 2

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Light orbiting a black hole is always unstable, as if it is balanced on a knife-edge. It will eventually either fall in (possibly spiraling), or out to infinity.

In fact more exotic three-dimensional orbits are possible around a spinning black hole. I have made animations of some of these here (there are also particle orbits but everything is labeled).

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But what happens when they cross the event horizon? Do they spiral down to singularity?

Light ray (rather than a photon), crossing black hole's horizon spiral in a sense. During its motion until final instant, r=0, it covers an angle not bigger than Pi!

Such an angle is not bigger than Pi also for other kinds of Black Holes: Reissner-Nordstroem, Kerr one or Kerr - Newman one.

Andrzej Radosz

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