The manifold is well-behaved and continuous at r=1, and mass is one of the few characteristics a black hole has other than spin and charge. Gravitons from within the event horizon won’t escape, but the event horizon itself can be thought of as the entire black hole (for everything outside of the black hole).

This discussion might help where my ability to answer your excellent question is failing: https://physics.stackexchange.com/questions/937/how-does-gra...