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Imagine an infinite empty space except for a local mass distribution resembling our observable universe. I don't think there lies no mass behind the horizon but let's imagine that this is the case. The event horizon lies outside of this local universe and it might be clear that black holes are present in this universe. Can we say that black holes can reside in black holes?

Qmechanic
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MatterGauge
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    Why is there a horizon in that setup? – PM 2Ring Feb 21 '22 at 08:47
  • Inside the event horizon of a black hole (here I mean static one for simplicity), the radial and time dimension are exchanged, meaning that there can't be a universe inside a black hole in the first place because everything will be concentrated into the singularity. – Jeanbaptiste Roux Feb 21 '22 at 08:49
  • @JeanbaptisteRoux You can put a FLRW universe (of finite size) inside a black hole. One simple model of black hole formation involves what amounts to a collapsing FLRW universe whose big crunch singularity is also the black hole singularity. – benrg Feb 21 '22 at 09:00
  • @PM2Ring Why not? The event horizon of all mass in the visible universe lies outside of the universe. – MatterGauge Feb 21 '22 at 09:01
  • FWIW, one of the best posts on cosmological horizons is https://physics.stackexchange.com/a/63780/123208 – PM 2Ring Feb 21 '22 at 09:08
  • @benrg Thanks for the clarification. Have you any papers related to this model? – Jeanbaptiste Roux Feb 21 '22 at 09:15
  • @PM2Ring Thanks for the link. Someone called the answer "philosophical babble"... Why is that? Why can't velocity be defined in curved spacetime? Because varying time and space metric? – MatterGauge Feb 21 '22 at 09:16
  • @Felicia Well, in GR you can always chop spacetime up into small chunks that have negligible curvature, and then do special relativity inside the chunks. So velocity can be defined locally. The problems arise when you try to stitch the chunks together so that you can define global times, distances, velocities, and energies. It comes down to the fact that in a curved space parallel transport gets messed up. https://en.wikipedia.org/wiki/Parallel_transport – PM 2Ring Feb 21 '22 at 09:43

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There are solutions in General Relativity in which you can cross more than you event horizon and perhaps find a lot of structure beyond the horizon. For example, the well known Reissner–Nordström and Kerr black holes have a "tower" of event horizons. After you cross the first one, you still have infinitely many event horizons you can keep crossing. This can be seen from their Penrose diagram and is very well exemplified in PBS Space Time's video Mapping the Multiverse.

I should point out, however, that these "inner horizons" concern the maximal extensions of these spacetimes and there are physicists who believe this mathematical procedure to be unphysical. Hence, I believe an adequate answer for your question would be:

General Relativity does allow for these sorts of solutions, but since we have no way of probing inside a black hole's event horizon we can't really tell whether they are physical or not.

Níckolas Alves
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