Shock Wave Interactions in General Relativity: A Locally Intertial Glimm Scheme for Spherically Symmetric Spacetimes: A Locally Intertial Glimm Scheme for Spherically Symmetric Spacetimes

Jeffrey Groah, Joel Smoller, Blake Temple038735073X, 9780387350738, 9780387446028

This monograph presents a self contained mathematical treatment of the initial value problem for shock wave solutions of the Einstein equations in General Relativity. The first two chapters provide background for the introduction of a locally intertial Glimm Scheme, a non-dissipative numerical scheme for approximating shock wave solutions of the Einstein equations in spherically symmetric spacetimes. What follows is a careful analysis of this scheme providing a proof of the existence of (shock wave) solutions of the spherically symmetric Einstein equations for a perfect fluid, starting from initial density and velocity profiles that are only locally of bounded total variation. The book covers the initial value problems for Einstein’s gravitational field equations with fluid sources and shock wave initial data. It has a clearly outlined goal: proving a certain local existence theorem. Concluding remarks are added and commentary is provided throughout. The book will be useful to graduate students and researchers in mathematics and physics.

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Table of contents :
front-matter……Page 1
1Introduction……Page 8
2The Initial Value Problem in Special Relativity……Page 26
3A Shock Wave Formulation of the Einstein Equations……Page 58
4Existence and Consistency for the Initial Value Problem……Page 78
back-matter……Page 151