In General Relativity (which is the theory we have to use if we're talking about black holes), gravity is not a force, it's spacetime curvature. The spacetime c

In General Relativity (which is the theory we have to use if we're talking about black holes), gravity is not a force, it's spacetime curvature. The spacetime curvature at any point in spacetime depends only on the matter in the past light cone of that point. Heuristically, "gravity" travels at a finite speed in GR. But there is matter and energy everywhere in the universe, so there is spacetime curvature everywhere; there is no place you can go to "escape" from its effects. So thinking of gravity as a Newtonian "attraction over infinite distance" doesn't really work in GR, but neither does thinking of it as a "force" with a finite range. It works differently from either of those.