  The mathematics of general relativistic shock waves is introduced and
considered in a cosmological context. In particular, an expanding
Friedmann-Roberson-Walker metric is matched to a Tolman-Oppenheimer-Volkoff
metric across a spherical shock surface. This is the general relativistic
analogue of a shock-wave explosion within a static singular isothermal fluid
sphere and may be regarded as a model for the Big Bang. These shock waves are
constructed both within and beyond the Hubble radius, which corresponds to a
universe outside and inside its Schwarzschild radius respectively. Certain
self-similar perturbations of the FRW metric lead to an accelerated expansion,
even without a cosmological constant, and thus it is conjectured that such a
mechanism may account for the anomalous acceleration observed today without
recourse to dark energy.
