I've been wrestling with this same problem, and can't find a satisfying answer. One problem I have with the usual description of a black hole is that the singul

I've been wrestling with this same problem, and can't find a satisfying answer. One problem I have with the usual description of a black hole is that the singularity is at the center. But it seems to me that if the escape velocity is the speed of light at the Schwarzschild radius, then the singularity should be there. More of a spherical asymptote than a point mass in the center.