How does Hawking radiation occur if time stops at a black hole's event horizon?

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Abishek
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In the view of Hawking radiation and entropy of black holes, the evaporation is continuous and at one point, there will be no singularity for the black hole. By relativity, if we reach a super massive black hole, then time would be relatively slowed down to a point that it stops (maybe?). Now, if there is no "time" for occurrence of Hawking radiation, then how does it actually occur? Even if it did occur, then will it not be a very slow process?

P.S: I am ready for the stabs of cruel physics professors now...
 
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The formulas are calculated for time as seen by an observer far away - for large black holes, it is a very slow process because the temperature is tiny, but for small black holes it is fast.
 
To expand just slightly on mfb's response, what he has pointed out indirectly is that LOCALLY, at the position of the black hole, time passes normally, it does not slow down much less stop.
 
Abishek said:
It's hard to visualize...
We humans have evolved in an INCREDIBLY limited range of physical phenomena so there are TONS of things in cosmology (the very large) and quantum mechanics (the very small) that we find "hard to visualize" (and a lot of it just flat hard to believe).