SHOCK WAVE COSMOLOGY INSIDE A BLACK HOLE: THE CASE OF NON-CRITICAL EXPANSION

Abstract

We derive and analyze the equations that extend the results in [20,21] to the case of non-critical expansion k≠0. By an asymptotic argument we show that the equation of state [Formula: see text] plays the same distinguished role in the analysis when k≠0 as it does when k=0: only for this equation of state does the shock emerge from the Big Bang at a finite nonzero speed — the speed of light. We also obtain a simple closed system that extends the case [Formula: see text] considered in [20,21] to the case of a general positive, increasing, convex equation of state p=p(ρ).