In classical general relativity, a freely falling observer can cross the event horizon of a black hole in finite proper time. However, from the perspective of a distant observer, the falling object appears to asymptotically approach the horizon due to gravitational time dilation, never actually crossing it.
Now, considering Hawking radiation: Every black hole evaporates in finite external time due to this effect. This raises an interesting question:
Can the infalling observer ever truly cross the event horizon if the black hole evaporates in finite external time? If yes, what happens to the observer when the black hole completely evaporates? If no, does this imply that no one can ever actually fall into a black hole in a physical sense? It seems that if the black hole evaporates "too quickly" from the perspective of an external observer, the event horizon may cease to exist before the falling object can ever reach it. Are there any known papers or calculations addressing this problem?
