Is a Black Hole a Surface?

Bobby asks whether a black hole has a surface in the sense of like having a physical hard surface on which you can actually stand or to which you would crash if you fell into it. The way to think about this is in terms of the forces. We don't think there's anything that can overcome the power of gravity once you are inside the black hole. That's why general relativity predicts a singularity. It says that things just keep compressing and compressing until you get a dot of infinite density.