Springer Monographs in Mathematics

Shock Wave Interactions in General Relativity

A Locally Inertial Glimm Scheme for Spherically Symmetric Spacetimes

Authors: Groah, Jeffrey, Smoller, Joel, Temple, Blake

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  • ISBN 978-0-387-44602-8
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About this book

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.

Table of contents (4 chapters)

Table of contents (4 chapters)
  • Introduction

    Pages 3-20

  • The Initial Value Problem in Special Relativity

    Pages 21-52

  • A Shock Wave Formulation of the Einstein Equations

    Pages 53-72

  • Existence and Consistency for the Initial Value Problem

    Pages 73-145

Buy this book

eBook 85,59 €
price for Spain (gross)
  • ISBN 978-0-387-44602-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Hardcover 103,99 €
price for Spain (gross)
Softcover 103,99 €
price for Spain (gross)
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Bibliographic Information

Bibliographic Information
Book Title
Shock Wave Interactions in General Relativity
Book Subtitle
A Locally Inertial Glimm Scheme for Spherically Symmetric Spacetimes
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2007
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-44602-8
DOI
10.1007/978-0-387-44602-8
Hardcover ISBN
978-0-387-35073-8
Softcover ISBN
978-1-4419-2246-5
Series ISSN
1439-7382
Edition Number
1
Number of Pages
VIII, 152
Number of Illustrations
7 b/w illustrations
Topics