We know that since photons are massless, . Consider a photon moving outward radially. We can compute the radial velocity in the Schwarzschild coordinates.
This solution in the normal spherical coordinates has a singularity. It is unclear what happens for . When analyzed in coordinates without this singularity, we find that photons will be pulled to if they start out with . This is of course the phenomenon of the Black Hole. No light can come out.
A collapsing star is seen from the outside to take an infinite amount of time to collapse down to the Schwartzchild radius due to the gravitational effect on time. So, from the outside, a black hole is matter nearly at the Schwartzchild radius, plus some matter that was already inside that radius when the star collpsed. According to GR, the black hole collapses down to a point, but we have no way of ever measuring that from the outside.
Jim Branson 2012-10-21