ASTROPHYSICAL SHOCK-WAVE SOLUTIONS OF THE EINSTEIN EQUATIONS

We construct exact, spherically symmetric, shock-wave solutions of the Einstein equations for a perfect fluid. The solutions are obtained by matching a Friedmann-Roberson-Walker metric (a cosmological model for the Universe) to a static Oppenheimer-Tolman metric (a model for the interior of a star) across a shock-wave interface. This is in the spirit of Oppenheimer and Snyder, except, in contrast with the Oppenheimer-Snyder model, the pressure p is nonzero. Our shock-wave solutions model the general relativistic version of an explosion into a static, singular, isothermal sphere. Shock waves introduce time irreversibility, loss of information, decay, dissipation, and increase of entropy into the dynamics of a perfect fluid in general relativity. As a corollary, we also obtain a different Oppenheimer-Snyder model for the case p==0. © 1995 The American Physical Society.