Shock Wave Interactions in General Relativity

A Locally Inertial Glimm Scheme for Spherically Symmetric Spacetimes

Jeffrey Groah, Joel Smoller, Blake Temple - Collection Springer Monographs in Mathematics

158 pages, parution le 29/01/2007

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Résumé

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 inertial 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.

Sommaire

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

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Jeffrey Groah, Joel Smoller, Blake Temple
Collection	Springer Monographs in Mathematics
Parution	29/01/2007
Nb. de pages	158
Format	16 x 24
Couverture	Relié
Poids	350g
Intérieur	Noir et Blanc
EAN13	9780387350738
ISBN13	978-0-387-35073-8