  We construct exact, entropy satisfying shock wave solutions of the Einstein
equations for a perfect fluid which extend the Oppeheimer-Snyder (OS) model to
the case of non-zero pressure, {\it inside the Black Hole}. These solutions put
forth a new Cosmological Model in which the expanding
Friedmann-Robertson-Walker (FRW) universe emerges from the Big Bang with a
shock wave at the leading edge of the expansion, analogous to a classical shock
wave explosion. This explosion is large enough to account for the enormous
scale on which the galaxies and the background radiation appear uniform. In
these models, the shock wave must lie beyond one Hubble length from the FRW
center, this threshhold being the boundary across which the bounded mass lies
inside its own Schwarzshild radius, $2M/r>1,$ and thus the shock wave solution
evolves inside a Black Hole. The entropy condition, which breaks the time
symmetry, implies that the shock wave must weaken until it eventually settles
down to a zero pressure OS interface, bounding a {\em finite} total mass, that
emerges from the White Hole event horizon of an ambient Schwarzschild
spacetime. However, unlike shock matching outside a Black Hole, the equation of
state $p=\frac{c^2}{3}\rho,$ the equation of state at the earliest stage of Big
Bang physics, is {\em distinguished} at the instant of the Big Bang--for this
equation of state alone, the shock wave emerges from the Big Bang at a finite
nonzero speed, the speed of light, decelerating to a subluminous wave from that
time onward. 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 an asymptotically flat Schwarzschild spacetime.
