Hello. I've had a question in the back of my mind about black holes for a while now. I asked my astronomy professor (who's a pretty smart guy), and he basically said that since he's not an expert on black holes, there's a lot about them that even he doesn't understand and he didn't know the answer to my question.

So it goes like this: As you fall towards the event horizon of the black hole, time dialation will slow down the passage of time. Or, for the unfortuante infalling astronaut, he will see the time for the rest of the universe speed up. Now the equations work out such that time dialation becomes infinte at the event horizon. This means that for any outside observer looking at a black hole, infalling matter will take an infinite amount of time to reach the even horizon of the black hole.

This is more then just an optical illusion, however. The personal time of infalling matter is actually slowing down (please note that I have no problem with this, my question is still coming ). Now, normally this wouldn't be a problem. The infalling matter may take longer to reach the black hole (it'll take forever in fact), however it will still be adding it's mass to the overall gravitational well of the black hole. A spacecraft orbiting the black hole won't notice a difference in it's orbit weather the matter is hovering a few millimeters about the event horizon or actually inside it.

We also know that black holes can evaporate. While this takes an extremly long time to happen, It still takes much less time then infinity. So here is my question:

If it takes an infinite amount of time for a chunk of matter to reach the event horizon of a black hole, and the black hole will evaporte completely in less time then that, wouldn't that mean that any matter falling towards a black hole won't acutally reach the event horizon? The black hole should evaporate completely before you ever get there!

Anyone have any thoughts on this?