As one falls into a black hole a person, or object, would experience a greater and greater time dilation caused by the gravitational field. At the point that one reaches the event horizon, Einstein's equations show that one's relativistic time dilation would stretch towards infinity.
Whilst your own experience of time passing would not change - your clock would seem to still be ticking along normally, the entire future of the universe would pass in an infinitely small period of your time. As you approached the event horizon time in the rest of the universe would seem to be passing faster and faster and if we apply Zeno's Paradox to this situation and examine our situation as we repeatedly halve our distance to the event horizon we would find that we have a situation where in a finite time passing for us the rest of the universe would appear to go through an infinite amount of time. In fact we would have to conclude that we would never reach the event horizon because an infinite amount of time can never pass in the distant reaches of the universe where there is no gravitational field.
I thought that maybe we could discount this because everywhere there will be at least a tiny gravitational effect from our black hole... but what if the entire universe contained just two black holes, us and one other observer, exactly half way between?
So again Zeno shows us that space and time must be quantised. At some point we reach some minimum distance or time away from the event horizon and after one more tick of time we MUST reach the horizon.
But then what? The infinite future of the universe cannot tick away in the next quantum of time because Hawking has shown us that that must include the evaporation of the Black Hole - how on earth does that affect us? (Edit: Assuming it is not gaining mass quicker than it is evaporating away). I'm starting to involve a lot of concepts now and losing track of how each affects each other but I cannot see how any combination of them can prevent us from still being on the event horizon of that black hole as it, potentially the only mass in the universe, evaporates. Maybe this is the fate of the universe... one black hole, constantly radiating and regathering it's energy/mass/entropy... but still what of our observer stuck on the event horizon?
Perhaps I've just (re)discovered a reason why Relativity and Quantum Physics don't combine but this seems unsurmountable... unless I've missed something. The only thing I can think of is that Zeno was wrong and there is no quantum of time or space (I don't actually think this is true - it's just the only thing I can come up with so far)... in which case no matter would ever reach the event horizon of a black hole. Unfortunately since the gravitational attraction of a shell is the same as that of a sphere, everywhere except inside it, we'd never be able to tell from gravity measurements. It would explain something interesting though... it's a reasonably well held theory that the Universe itself is a Black Hole and hence no mass can get inside it after its formation... the looking glass goes deeper!
Anyone care to enlighten me? Very tempting to want to fall into a black hole now and find out what happens! I won't be able to tell you of course but at least I'll know!