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There are Two different defintions for the event horizon of a black hole. The Absolute horizon and the Apparent horizon. An apparent horizon is a surface that is the boundary between light rays that are directed outwards and moving outwards and those directed outward but moving inward. While and Absolute Horiozn is a boundary defined with respect to the external universe, inside which events cannot affect an external observer at infinity. Normally these horizons coincide but they can differ during event such ad black hole mergers.

Technically, knowing exactly where the Absolute horizon is requires knowing the entire future history of spacetime. So it seems to me therefore that in a universe destined to even in a big crunch, black holes wouldn't technically have Absolute horizons, only Apparent horizons.

blademan9999
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  • Your conclusion is unclear. If you know the entire history of the universe up to the moment of the Big Crunch, you can figure out where the event horizon is today. Why not? – safesphere Jul 28 '23 at 15:42
  • Because you can never escape to infinity? – blademan9999 Jul 28 '23 at 15:42
  • Consider an example of a hollow shell collapsing to a black hole. A flashlight in the center emits a beam of light right now. Will this light escape to “infinity” (meaning escapes being trapped inside the shell) or will it end up hitting the singularity? In other words, is this light already inside the event horizon before the shell has collapsed? The answer depends on what happens next, depends on the future. If the shell keeps collapsing, the light gets trapped. If the collapse stops for any reason, the light escapes. Whether or not this light escapes actually to “infinity” is irrelevant. – safesphere Jul 28 '23 at 16:02
  • " This is the set of points which are approached asymptotically by null rays (light rays, for example) which can escape to infinity." from https://en.wikipedia.org/wiki/Absolute_horizon#Definition – blademan9999 Jul 28 '23 at 16:03
  • You cannot take “infinity” here literally. It simply means far enough from the system to where the effects of the system become negligible. Note that nothing can escape actually to infinity, because infinity is not a point, which anything could ever reach. See my example above. If the light escapes to outside of the shell, then the absolute horizon did not exist inside the shell when the light was emitted. The further travel of this light towards infinity is completely irrelevant to the existence of the horizon despite the generality of the definition trying to account for all possible cases. – safesphere Jul 28 '23 at 17:10

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