Let's assume an observer looking at a distant black hole that is created by collapsing star.
In observer frame of reference time near black hole horizon asymptotically slows down and he never see matter crossing event horizon. So black hole is visible as some kind of frozen object - falling matter almost stops near horizon and light emitted or reflected by it becomes more and more redshifted as it approaches horizon.
On the other hand black hole emits thermal radiation that causes it's evaporation. After some time it will finally disappear.
As these two points seems extremely incompatible with each other, my question is how transition from such frozen object to state of no black hole (complete evaporation) looks for distant observer?
What I'm curious about is where this Hawking radiation comes from. I suppose it will be surface of the horizon, but in fact from observer frame of reference there is nothing at this surface yet - matter didn't fall on it yet, it's just approaching it asymptotically.
What is strange from classical point of wiew is how Hawking radiation can be visible being emitted from place where there is nothing? Or what's more interesting how the matter observer see falling on BH will dissappear as evaporation is in progress?