Shock-wave cosmology inside a black hole

We construct a class of global exact solutions of the Einstein equations that extend the Oppeheimer-Snyder model to the case of nonzero pressure, 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 be-hind 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 Oppenheimer-Snyder interface, (bounding a 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 cosmological model in which the big bang arises from a localized explosion occurring inside the black hole of an asymptotically flat Schwarzschild spacetime.