Is There a Surface to the Black Hole?

There's definitely like an edge to a black hole in the sense that we can say there's a point of no return. If you get closer to the black hole than this, then all paths lead towards the center. The only way to know if you're past the event horizon is to do the calculations and see if there's any path out for any particle even into the infinite future. So what you see when you look at a black hole is not the actual physical extent of the black hole, but an image of the blackhole that's been distorted by these weird past that light follows.