Shock-wave explosions in general relativity

In earlier work the authors constructed a class of spherically symmetric, fluid dynamical shock-waves that solve the Einstein equations of general relativity. These shock-waves extend the celebrated Oppenheimer-Snyder result to the case of non-zero pressure. In general our shock-waves are determined by a system of ordinary differential equations (ODE^s) that describe the matching of a FriedmannRobertson-Walker metric, (a cosmological model for the expanding universe), to an Oppenheimer-Tolman metric, (a model for the interior of a star), across a shock interface. A global exact solution of these ODE'S was found for isothermal equations of state, and in this exact solution, the Big Bang begins with a shock-wave explosion instead of the usual singularity of cosmology. In this talk we discuss new work of the authors in which we derive an alternate version of the general ODE'S, and we use these to demonstrate that our theory generates a large class of physically meaningful outgoing (Lax admissible) shock-waves that model blast waves in a general relativistic setting. We also obtain formulas for the physical quantities that evolve according to the equations. The resulting formulas are important for the numerical simulation of these solutions.