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I've just been reading Steven Hawking's The Universe in a Nutshell and it talks a lot about black holes.

It says that no-one in the external universe would see any matter cross the event horizon of a black hole because of time dilation. The matter crossing the event horizon does cross it in its own time frame but would observe the entire history of the universe as it goes by.

However it seems to me that the matter never crosses the event horizon. This is why:

The outside observer sees the black hole evaporate in a finite time by Hawking radiation. Given that it takes infinite time (seen from an outside observer) to cross the event horizon, the black hole evaporates before the matter ever crosses the event horizon.

Thus nothing ever falls into a black hole.

Is this reasoning correct? I'm not entirely sure.

No: the fact that light of the disappearing object hasn't reached your eyes, doesn't mean it hasn't disappeared.

In other words: Just before the black hole ceases to be a black hole, the light coming towards you from the disappearing object is blue-shifted again, and you'll see the object disappear just before the black-hole itsself changes into whatever it want's to change into.

From http://antwrp.gsfc.nasa.gov/htmltest/gi ... b_faq.html:

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.)