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First, a brief introduction to provide the right context. I've been studying General Relativity with Ohanian and Ruffini's Gravitation and Spacetime. They introduce Kruskal-Szekeres coordinates for Schwartzschild spacetimes in Section 8.3 (Maximal Schwarzschild geometry) and show a spacetime diagram in such coordinate system:

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Then, somewhere later, it reads:

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In particular, they say "This second space is in a different universe; alternatively, it may be regarded as a region in our own universe, if this second region of our universe is very far away from the first." and "However, if astronauts from both universes jump into the black hole (region II), then they can meet, embrace, and perish together." I'm not sure I got it right but I infer two possibilities:

  • the same black hole exist in both universes; or
  • the same black hole exists in two different regions of the same universe.

Is this correct? If so, what are the implications? Should we expect an unidentified grow of the black hole's size as there would be invisible matter (from our point of view) from the other universe (or region of our own) falling into the black hole?

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the same black hole exist in both universe

Yes, this is correct.

Should we expect an unidentified grow of the black hole's size as there would be invisible matter (from our point of view) from the other universe [...] falling into the black hole?

The Schwarzschild spacetime describes an eternal black hole: one that has always existed and always will exist. It doesn't describe a black hole that has formed by gravitational collapse. For the case of an actual astrophysical black hole, which formed by gravitational collapse, only regions I and II exist.

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  • $\begingroup$ Thanks for the clarification! Is there any observational signature that distinguishes eternal black holes from astrophysical ones? (Or could you suggest some reading material about it?) $\endgroup$ – andrehgomes Mar 13 '18 at 13:53
  • $\begingroup$ @andrehgomes: An eternal black hole is a purely theoretical object. It can't exist because our universe hasn't existed for an infinite amount of time. $\endgroup$ – Ben Crowell Mar 14 '18 at 22:40
  • $\begingroup$ I found in Ohanian & Ruffini's book (some pages after the quoted text in the OP) that "Since the complete Kruskal diagram is irrelevant for black holes formed by gravitational collapse, it can apply only to black holes created jointly with the universe, that is, black holes that have existed ever since the beginning of time." Is this at odds with what you said or am I missing something? $\endgroup$ – andrehgomes Mar 15 '18 at 11:27

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