  We argue that the formation of a Schwarzschild black hole via
Datt-Oppenheimer-Snyder type gravitational collapse must be accompanied by a
change in topology upon formation of the event horizon which physically
separates matter in the interior from that of the exterior. While it is true
that collapsing matter crossing the event horizon continues to fall towards the
singularity of the Schwarzschild interior, this region does not in fact contain
the matter originally responsible for the collapse. Rather, the latter occupies
a distinct internal spacetime region with its own independent evolution. The
existence of this additional component of the simplest black hole has a number
of profound implications - Schwarzschild black holes are stable with constant
mass; they each contain a self-contained mini-universe within their event
horizons; and they live within a spacetime that is inherently double-sheeted.
