Shock Wave Interactions in General Relativity: A Locally Inertial Glimm Scheme for Spherically Symmetric Spacetimes / Edition 1

Shock Wave Interactions in General Relativity: A Locally Inertial Glimm Scheme for Spherically Symmetric Spacetimes / Edition 1

by Jeffrey Groah, Joel Smoller, Blake Temple
     
 

ISBN-10: 038735073X

ISBN-13: 9780387350738

Pub. Date: 11/30/2006

Publisher: Springer New York

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

Overview

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.

Product Details

ISBN-13:
9780387350738
Publisher:
Springer New York
Publication date:
11/30/2006
Series:
Springer Monographs in Mathematics Series
Edition description:
2007
Pages:
152
Product dimensions:
6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

Introduction.- The Initial Value Problem in Special Relativity.- A Shock Waves Formulation of Einstein Equations.- Existence and Consistency for the Initial Value Problem.- Bibliography.

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