“As I understood it, the mathematical point at which light cannot escape corresponds to the mathematical point where time effectively stops for matter. If that’s not the case, then that’s what I’d like to know.”
No. We observe gravitational fields in relation to velocity but that’s not what is happening (according to the guys with higher IQs than me). The gravity field is so powerful, it is bending spacetime. Time is still moving at a slower rate to the outside observer (normal to the unlucky person in the event horizon) and the gravitational forces are tearing all mass apart. Read ‘Death by Black Hole’ by Neil deGrasse Tyson about spaghettification :)
At the point of singularity itself, time has reached zero.
http://en.wikipedia.org/wiki/Gravitational_singularity
Read Types - Curvature for the mathematics about it.
Yes, and if time has stopped at the singularity, it’s nearly stopped just outside of the singularity so how does anything actually ever reach the singularity?