Title:  Cosmology, Black Holes, and Shock Waves Beyond the Hubble
Length

                                          By Joel Smoller
Abstract :
   In this talk, we present, in a rigorous mathematical setting, a new
Cosmological Model in which the expanding
Friedmann-Robertson-Walker (FRW) universe emerges from an event
more similar to a classical explosion---there is a shock wave at
the leading edge of the expansion---than the standard scenario of
the Big Bang.  We believe that General Relativity (GR) pretty much
forces such a solution on you as soon as you try to relax the
assumption in the standard model that the expansion of the
galaxies is of infinite extent at each fixed time.  (You could say
that in our model, the Copernican Principle is replaced by  the
principle in physics, that nothing is infinite.)
   Most importantly, in these new models, the explosion is large enough to
account for the enormous scale on which the galaxies and the
cosmic background radiation appear uniform.
   There are a number of remarkable twists that arise in these new GR
blast waves.  First of all, the shock wave lies beyond one Hubble
length from the FRW center, this threshold being the boundary
across which the bounded mass lies inside its own Schwarzschild
radius---that is, 2M/r>1 beyond one Hubble length---and thus the
shock wave solution evolves inside a Black Hole.  The nature and
evolution of the "total mass" inside the Black Hole is unexpected
and interesting.
   Another interesting consequence is that the entropy condition chooses
the explosion over the implosion, (time irreversibility), and also
implies that the shock eventually weakens until it emerges from
the Black Hole, (through the White Hole event horizon), as a zero
pressure Oppenheimer-Snyder solution.  Asymptotically, for large
time, the explosion settles down to something like a giant
supernova of finite mass and extent, but on an enormous scale---a
localized mass expanding into an asymptotically flat Schwarzschild
spacetime, everywhere outside the Black Hole.
   But he biggest surprise to us is that unlike shock matching outside the
Black Hole, the equation of state, p=(1/3)(rho)---the equation of
state at the earliest stage of Big Bang physics---is distinguished
at the instant of the Big Bang. Namely, for this equation of state
alone, the shock wave emerges from the Big Bang at a finite
nonzero speed, the speed of light. (The shock wave then
decelerates to a sub-luminous wave at all times after the Big
Bang.)
   These solutions describe, in exact formulas, the global dynamics of
strong gravitational field solutions  of the Einstein equations,
and the setting, inside the Black Hole, is pretty much unexplored
territory for analysis.
   (This paper describes joint work with Blake Temple, University of
California, Davis