On the contrary, you can’t do anything but catch up to it. As you get closer to the event horizon, the space gets warped so much that the blackness actually takes up more of your field of view than the horizon. So visually if you were really close to the event horizon, everything around you besides the horizon would be squished into a circle above, while the blackness below you would surround it. Once you pass the horizon, the bottom completely dominates your field of view. Now every direction becomes down. This is what is meant by the time and space switcheroo. No matter which way you fire your thrusters, you’ll go in the direction of the singularity, so at that point it’s only a matter of time.
Blackholes have a finite life, correct? Shouldn’t we be able to observe some change when the blackhole eventually poofs out of existence?
Do you want the classical answer, the semiclassical answer, or the quantum answer?
The classical answer is that the remnants of the star have no problem falling in, because in their reference frame, it takes a finite amount of time. From our reference frame, it takes an infinite time, but that doesn’t matter, because we’re not the ones falling in. Nor do you have to worry about the black hole ceasing to exist before anything actually makes it in, because black holes last forever.
The semiclassical answer is that, no, black holes don’t last forever in the external reference frame, so anything that’s going to make it in has to do so in a finite time, also as measured in the external reference frame. However, in this view, there are various sorts of fluctuations always going on at the surface of the black hole (and, in fact, everywhere in spacetime), and that those quantum fluctuations are the reason that the black hole gradually evaporates. These same fluctuations also mean that the event horizon of the black hole can’t be precisely localized, so getting almost all the way to the horizon really is good enough, and we can’t take words like “never” quite literally when we’re looking at time scales immense enough for the black hole to evaporate.
The quantum answer would tell us just what does happen to the infalling matter, and how and when it crosses the boundary, and the like. Unfortunately, nobody knows what the quantum answer is.
Something that helps get a handle on the “what does it look like” questions is to think of two different parts of the system. We’ve got the space ship falling in towards the hole, and we’ve got the photons the ship emits trying to climb away from the hole. Once the ship crosses the event horizon, the photons can’t move fast enough to get farther away. But they’re slowed down and stretched out even before that point.
What helps in understanding is to forget about the ship and just think about a gun that’s held automagically some distance away from the hole. The closer the gun sits to the hole, the slower its photons move at first, and the more they get stretched out by the hole’s gravity during their climb. When the gun is sitting just a tiny bit above the event horizon, it takes an incredibly long time for those photons to escape back to an observer far away.
Now think of the ship falling in and triggering a series of these guns as it goes. From the ship’s perspective it’s triggering the guns at a steady rate, like once per second. But each one is closer and closer in towards the hole, so its photon takes longer to escape, and so events the ship sees one second apart take longer and longer to reach us, and are spaced out farther and farther than one second.
Now just forget the guns, and think of the photons emitted by the ship’s running lights. And that’s why the ship looks to be moving slower and slower. The last photons it emits take forever to reach the distant observer, and it seems to be frozen just above the event horizon.
Hmm. This may be a more profound statement then on the face of it. I’ll have to ponder on it for awhile. The only problem is Discontinuity keeps popping up. It’s almost like in our world nothing can get in, but that doesn’t matter because the stuff falling in is in that world over there.
Thanks
True. But the ship doesn’t just look like it’s moving slower, in our frame it really is moving slower.
As I said above drop down to the EH and then return to the rocket. There will be a very real difference in the passage of your and the rocket’s time
So falling schlub just slows down and never goes poof (to FAO’s POV)? I’m struggling with this. Why then don’t we see a ‘ring’ of debris of all of the things that have been gobbled up by the black hole around the EH?
Because just outside the horizon the photons have been slowed and red shifted to almost zero energy. And at the horizon they’re in a trapped null surface. The stuff is there but it can’t be seen in our FoR.