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I base my question on the following premise: from the perspective of an outside observer nothing can ever enter a black hole, due to the time dilation.

If that premise is true, then why the information paradox is even considered a paradox, since no information can enter black hole in a finite amount of time, whereas the black hole itself will cease to exist within a finite timeframe? So from the perspective outside of Schwarzschild radius of a black hole nothing is lost (since it freezes in time), and from the perspective of someone falling into a black hole no information is lost as well, since it is kind of taken along beyond event horizon?

Lugi
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  • Not really, since the answers seem incomplete, or straight up ignoring the fact that from an outside perspective nothing can get inside the black hole. This is why I put emphasis on that premise, and also made distinction between two scenarios, and that in none of them any information is lost. – Lugi Jun 03 '22 at 16:14
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    The accepted answer to this question Can black holes form in a finite amount of time?, explains why your premise that "from the perspective of an outside observer, nothing can ever enter a black hole" is flawed, due to the non-existence of a global notion of simultaneity in GR. – Paul T. Jun 03 '22 at 16:37
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    @PaulT. The referred answer of Ben Crowell is misleading and his Penrose diagrams are incorrect. The causality is well defined in GR, so the OP is correct, nothing enters a black hole in the coordinates of any external observer. The existence of “global notion of simultaneity” is not required to make this conclusion. Plus this “notion” is very easy to construct specifically for a Schwarzschild black hole. – safesphere Jun 04 '22 at 16:06
  • @Lugi You are misinterpreting the information paradox. It is not about the information lost inside a black hole. It is about the information lost outside the black hole after the black hole has evaporated. Nothing has crossed the horizon, but nothing is left while the Hawking radiation contains no information. Thus your question is based on a wrong premise. – safesphere Jun 04 '22 at 16:13
  • @safesphere But it has to be about the information lost inside the black hole, no? You can't just start with an eternal black hole that existed since the beginning of time, since in this case it wouldn't have any information to begin with. So in order for the information paradox to be valid something actually has to cross the even horizon in order to be lost in eventual evaporation due to Hawking radiation. – Lugi Jun 05 '22 at 19:02
  • @Lugi "something actually has to cross the even horizon in order to be lost in eventual evaporation" - Why? – safesphere Jun 06 '22 at 21:33

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