Astrophysical shock-wave solutions of the Einstein equations

Details Astrophysical shock-wave solutions of the Einstein equations Astrophysical shock-wave solutions of the Einstein equations

Mar 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phrvd..51.2733s&link_type=abstract

Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 51, Issue 6, 15 March 1995, pp.2733-2743

Mathematics

Logic

5

Exact Solutions, Einstein-Maxwell Spacetimes, Spacetimes With Fluids, Radiation Or Classical Fields

Scientific paper

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.

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