Mathematical Sciences: Problemss in Relativistic Fluids andEinstein-Yang/Mills Equations

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DMS-9501128 Smoller The principal investigator (PI) proposes to continue his investigations in the areas of shock waves in General Relativity, and Einstein- Yang/Mills (EYM) equations. He plans to study astrophysical shock waves modeling explosions, which are based upon matching of certain solutions of Einstein's equations across a shock-wave interface. Such shock wave solutions model stellar formation, and are related to a variety of astrophysical phenomena. The PI also plans to study, (together with A. Wasserman), certain solutions of the EYM equations modeling both black holes, and elementary particles. In particular, the black hole solutions are related to Hawking radiation of black holes. The principal investigator (PI) plans to study astrophysical shock wave solutions of Einstein's equations of General Relativity. These solutions model explosions and are related to stellar formation. Such solutions are also of interest in modeling quasars and can also be used to study cosmological models. The PI also will study the properties of black-hole and particle-like solutions which arise in the study of Einstein-Yang/Mills equations.