General Relativistic Shock Waves that Extend the Oppenheimer-Snyder Model

Abstract

In earlier work we constructed a class of spherically symmetric, fluid dynamical shock waves that satisfy the Einstein equations of general relativity. These shock waves extend the celebrated Oppenheimer-Snyder result to the case of non-zero pressure. Our shock waves are determined by a system of ordinary differential equations that describe the matching of a Friedmann-Robertson-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. In this paper we derive an alternate version of these ordinary differential equations, which are used to demonstrate that our theory generates a large class of physically meaningful (Lax-admissible) outgoing shock waves that model blast waves in a general relativistic setting. We also obtain formulas for the shock speed and other important quantities that evolve according to the equations. The resulting formulas are important for the numerical simulation of these solutions.