  We construct a class of global exact solutions of the Einstein equations that
extend the Oppeheimer-Snyder (OS) model to the case of non-zero pressure, {\em
inside the Black Hole}, by incorporating a shock wave at the leading edge of
the expansion of the galaxies, arbitrarily far beyond the Hubble length in the
Friedmann-Robertson-Walker (FRW) spacetime. Here the expanding FRW universe
emerges behind a subluminous blast wave that explodes outward from the FRW
center at the instant of the Big Bang. The total mass behind the shock
decreases as the shock wave expands, and the entropy condition implies that the
shock wave must weaken to the point where it settles down to an OS interface,
(bounding a {\em finite} total mass), that eventually emerges from the White
Hole event horizon of an ambient Schwarzschild spacetime. The entropy condition
breaks the time symmetry of the Einstein equations, selecting the explosion
over the implosion. These shock wave solutions indicate a new cosmological
model in which the Big Bang arises from a localized explosion occurring inside
the Black Hole of a Schwarzschild spacetime.
