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Consider a free-falling observer 1 approaching the event horizon of a black hole. Evaluating his proper time, one finds that he crosses the event horizon within finite time. For an asymptotic observer 2 however, the time it takes observer 1 to cross the event horizon is

*infinite*. However, the time it takes for the black hole to evaporate due to Hawking radiation is

*finite*. So observer 2 would see the black hole evaporate before observer 1 reaches the event horizon. Is that correct? And what would observer 1 see? The Universe, including the black hole accelerating in time so that the black hole vanishes in radiation before he can reach it?

Thank you for your answers.