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Black holes and time dilation question - Baleia espacial - 07-18-2021

Hello, hope you are all doing well, I have a question about what happens to things that aproach the event horizon of black holes, like, if time dilation increases as you or something aproach the black hole event horizon, wouldn't the "evaporation" of the black hole caused by hawking radiation become faster and faster until the black hole "evaporates" completely before you cross the event horizon and thus making it impossible to really get inside the black hole?