Topology change in spherical gravitational collapse

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.
Comment: 5 pages, 1 figure. To be presented at the 14th Marcel Grossmann Meeting, Rome, 12th-18th July, 2015