ENGLISH

Shock wave interactions in general relativity: a locally intertial glimm scheme for spherically symmetric spacetimes

By Jeffrey Groah , Joel Smoller , Blake Temple

Book information

Publisher
Springer
Year
2007
ISBN
9780387350738, 038735073X, 0387446028
Open Library ID
OL22743610M
Language
english
Format
PDF
Filesize
1 MB (1552044 bytes)
Series
Springer monographs in mathematics
Edition
1
Pages
156\156
Library
Kolxo3
Time added
2009-07-20 03:45:11

Description

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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