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＜E-Book＞
Shock Wave Interactions in General Relativity : A Locally Inertial Glimm Scheme for Spherically Symmetric Spacetimes / by Jeffrey Groah, Joel Smoller, Blake Temple
(Springer Monographs in Mathematics. ISSN:21969922)

Edition	1st ed. 2007.
Publisher	(New York, NY : Springer New York : Imprint: Springer)
Year	2007
Language	English
Size	VIII, 152 p. 7 illus : online resource
Authors	*Groah, Jeffrey author Smoller, Joel author Temple, Blake author SpringerLink (Online service)
Subjects	LCSH:Mathematics LCSH:Gravitation FREE:Applications of Mathematics FREE:Classical and Quantum Gravity
Notes	The Initial Value Problem in Special Relativity -- A Shock Wave Formulation of the Einstein Equations -- Existence and Consistency for the Initial Value Problem 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 HTTP:URL=https://doi.org/10.1007/978-0-387-44602-8

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