How does gravity work in a black hole?
I think the core of your question is “if a black hole is a hole, with no actual matter in it, how can it gravitate?” This is a very good question. It’s related to another question: “Ok, so the maximum speed for everything, including gravity itself, is the speed of light, and nothing can escape a black hole without exceeding the speed of light (which would be impossible). So how does gravity escape a black hole?” In fact, I asked this second question to Kip Thorne at a conference, back before I had learned general relativity. The answer is that the gravity outside the black hole is not the gravity from what we think of as the present, but it’s the gravity from eons ago, when the black hole formed from a neutron star or whatever. Time moves infinitely slowly at the horizon of a black hole, as seen from the outside. Also, light and gravity that’s emitted from the horizon takes an infinite amount of time to reach us. So spacetime still thinks there’s matter there! Also, a realistic black h