I'm looking for help in understanding how black holes can move through space. This is probably a trivial question for anyone who knows astronomy, but probably due to my lack of education on the topic, I can't come up with an answer or visualization on my own.
Specifically, my confusion is as follows:
I saw Dr. Kip Thorne in a documentary on black holes state that there is no longer any matter in a black hole once it forms. He said something like, the matter was there, but it has been crushed out of existence and basically has been transformed into the energy that produces such a great curvature of spacetime.
From that description, it seems to me that within the event horizon of a black hole it is simply this enormous "dent" in spacetime itself that is moving around.
I also saw Dr. Andrew Hamilton in another documentary state that within the event horizon of a black hole (again paraphrasing), space is falling toward the singularity so fast that it effectively drags everything with it (including light).
Based on 1 (no matter remains in the black hole) and 2 (space is being pulled towards the gravitational singularity from all directions), I try to picture the black hole moving, and it seems to me that if, say, the black hole moves in one direction, I can see how its event horizon is also moving, bringing that bit of space into it. But how can the other end of the black hole let space "escape" in order to complete the motion?
I am pretty sure I am just missing something here, because as I have learned, black holes have been found in galaxies and solar systems and many other places where they have to be moving. But I want to understand why it is that space itself can cross the event horizon when other things can't. And along those lines, it seems amazing to me that a black hole could be in essence a kind of scar in spacetime that can also move through it.
Thanks for any help and sorry for the wordy question.
UPDATE: Thanks for the answers so far. I hope someday I'll be able to comprehend them fully. :-)
I would like to add some further context that better illustrates my question.
If you go to the video here and watch the first minute or so (up to around 31:00)
you can see Andrew Hamilton explaining what I have a question about along with an animation to illustrate the description.
On the one hand, we have spacetime curved in such a way that the black hole structure remains intact - that is, there is a constant event horizon generated by that extreme curvature. But on the other hand, Dr. Hamilton describes a flow of spacetime between the event horizon and the inner horizon, and he says it is plausible that within that area, space itself (which has no substance, in his words) can be described as flowing in and being flung back out.
I don't understand how space can have these two opposing properties - (1) a curvature that is maintained in order for the black hole to exist, that is, a curvature generated because matter can interact with the space and (2) a flow of space that sounds like it is not subject to a restriction of crossing back out of the event horizon.
It's that apparent difference between (1) and (2) that I want to understand better.