http://apod.nasa.gov/htmltest/gifcity/bh_pub_faq.html#evaporate
5. What about Hawking radiation? Won't the black hole evaporate before you get there?
(First, a caveat: Not a lot is really understood about evaporating black holes. The following is largely deduced from information in Wald's GR text, but what really happens-- especially when the black hole gets very small-- is unclear. So take the following with a grain of salt.)
Short answer: No, it won't. This demands some elaboration.
From thermodynamic arguments Stephen Hawking realized that a black hole should have a nonzero temperature, and ought therefore to emit blackbody radiation. He eventually figured out a quantum- mechanical mechanism for this. Suffice it to say that black holes should very, very slowly lose mass through radiation, a loss which accelerates as the hole gets smaller and eventually evaporates completely in a burst of radiation. This happens in a finite time according to an outside observer.
But I just said that an outside observer would *never* observe an object actually entering the horizon! If I jump in, will you see the black hole evaporate out from under me, leaving me intact but marooned in the very distant future from gravitational time dilation?
You won't, and the reason is that the discussion above only applies to a black hole that is not shrinking to nil from evaporation. Remember that the apparent slowing of my fall is due to the paths of outgoing light rays near the event horizon. If the black hole *does* evaporate, the delay in escaping light caused by proximity to the event horizon can only last as long as the event horizon does! Consider your external view of me as I fall in.
If the black hole is eternal, events happening to me (by my watch) closer and closer to the time I fall through happen divergingly later according to you (supposing that your vision is somehow not limited by the discreteness of photons, or the redshift).
If the black hole is mortal, you'll instead see those events happen closer and closer to the time the black hole evaporates. Extrapolating, you would calculate my time of passage through the event horizon as the exact moment the hole disappears! (Of course, even if you could see me, the image would be drowned out by all the radiation from the evaporating hole.) I won't experience that cataclysm myself, though; I'll be through the horizon, leaving only my light behind. As far as I'm concerned, my grisly fate is unaffected by the evaporation.
All of this assumes you can see me at all, of course. In practice the time of the last photon would have long been past. Besides, there's the brilliant background of Hawking radiation to see through as the hole shrinks to nothing.
(Due to considerations I won't go into here, some physicists think that the black hole won't disappear completely, that a remnant hole will be left behind. Current physics can't really decide the question, any more than it can decide what really happens at the singularity. If someone ever figures out quantum gravity, maybe that will provide an answer.)
The numbers concerning fatal radii, dimming, and the time of the last photon came from Misner, Thorne, and Wheeler's _Gravitation_ (San Francisco: W. H. Freeman & Co., 1973), pp. 860-862 and 872-873. Chapters 32 and 33 (IMHO, the best part of the book) contain nice descriptions of some of the phenomena I've described.
Information about evaporation and wormholes came from Robert Wald's _General Relativity_ (Chicago: University of Chicago Press, 1984). The famous conformal diagram of an evaporating hole on page 413 has resolved several arguments on sci.physics (though its veracity is in question).
Steven Weinberg's _Gravitation and Cosmology_ (New York: John Wiley and Sons, 1972) provided me with the historical dates. It discusses some properties of the Schwarzschild solution in chapter 8 and describes gravitational collapse in chapter 11.
Posted to sci.astro frequently asked questions by Michael McIrvin.