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What's screwy is that black holes are only an issue for physics if they are eternal. As matter falls towards the event horizon, time, as measured from outside, goes ever slower. It takes an infinitely lon time to cross the event horizon. Hawking radiation means that it will never actually cross, since the black hole will retreat in a finite time. If you flew towards one, you would apparently skim it, without entering. You would emerge to find the universe long dead and gone however .
It turns black holes from problematic infinity points to really weird knots in spacetime.