As you approach a black hole, time slows down for you. Is it possible for the black hole to appear to decay via Hawking radiation as quickly as you fell in? Or does the decay occur too slowly for this?
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As you approach a black hole, time slows down for you.
Not true. Time always flows at its normal rate for you. You hit the singularity in about a millisecond in the case of a solar-mass black hole.
Related: What will the universe look like for anyone falling into a black hole? (but note that the accepted answer is wrong)