Actually,
the gravitational singularity
at the center of black holes
is probably NOT a point or ring of
infinite
density
as predicted by strict
general relativity.
It is believed that quantum gravity
must prevent collapse to
infinite
density.
The real counterpart to the
gravitational singularity
must be some exotic
quantum mechanical state, but
since we have NO established
quantum gravity theory, we do NOT
know what that state is.
However, Penrose's
is still valid for showing
that the event horizon exists.????
For more on the gravitational singularity,
see
IAL 25: Black Holes: Schwarzschild Black Holes: The Singularity.