3+1 Formalism in General Relativity : Bases of Numerical Relativity

Berlin, Heidelberg : Springer Berlin Heidelberg, 2012

Abstract/Sommario: Basic Differential Geometry -- Geometry of Hypersurfaces -- Geometry of Foliations -- 3+1 decomposition of Einstein Equation -- 3+1 Equations for Matter and Electromagnetic Field -- Conformal Decompositon -- Asymptotic Flatness and Global Quantities -- The Initial Data Problem -- Choice of Foliation and Spatial Coordiinates -- Evolution Schemes -- Conformal Killing Operator and Conformal Vector Laplacian -- Sage Codes. - This graduate-level, course-based text is devoted to the 3+1 form ...; [leggi tutto] Basic Differential Geometry -- Geometry of Hypersurfaces -- Geometry of Foliations -- 3+1 decomposition of Einstein Equation -- 3+1 Equations for Matter and Electromagnetic Field -- Conformal Decompositon -- Asymptotic Flatness and Global Quantities -- The Initial Data Problem -- Choice of Foliation and Spatial Coordiinates -- Evolution Schemes -- Conformal Killing Operator and Conformal Vector Laplacian -- Sage Codes. - This graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in space-time, foliation of space-time by a family of space-like hypersurfaces), and then turns to the 3+1 decomposition of the Einstein equations, giving rise to the Cauchy problem with constraints, which constitutes the core of 3+1 formalism. The ADM Hamiltonian formulation of general relativity is also introduced at this stage. Finally, the decomposition of the matter and electromagnetic field equations is presented, focusing on the astrophysically relevant cases of a perfect fluid and a perfect conductor (ideal magnetohydrodynamics). The second part of the book introduces more advanced topics: the conformal transformation of the 3-metric on each hypersurface and the corresponding rewriting of the 3+1 Einstein equations, the Isenberg-Wilson-Mathews approximation to general relativity, global quantities associated with asymptotic flatness (ADM mass, linear and angular momentum) and with symmetries (Komar mass and angular momentum). In the last part, the initial data problem is studied, the choice of spacetime coordinates within the 3+1 framework is discussed and various schemes for the time integration of the 3+1 Einstein equations are reviewed. The prerequisites are those of a basic general relativity course with calculations and derivations presented in detail, making this text complete and self-contained. Numerical techniques are not covered in this book [comprimi]

Copertina 3+1 Formalism in General Relativity : Bases of Numerical Relativity

Fonte: GOOGLE

Dettagli
Risorse digitali

Dettagli

Campo	Valore
Descrizione	3+1 Formalism in General Relativity : Bases of Numerical Relativity / by Eric Gourgoulhon. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2012. - XVII, 294p. 29 illus ; digital. - (Lecture Notes in Physics ; 846)
Specifiche	[Supporto spec. Risorsa elettr.] Risorsa remota
Note	Springer eBooks. - Printed edition: 9783642245244
Collezione	[Fa parte di] Lecture Notes in Physics ; 846 [Vai al dettaglio]
Altri legami	[Altra edizione di] 3+1 Formalism in general relativity : bases of numerical relativity / by Eric Gourgoulhon
Autori	Gourgoulhon, Eric - [Responsabilità principale] SpringerLink (Online service) - [Responsabilità secondaria]
Soggetto	Astronomy Astronomy, Astrophysics and Cosmology Classical and Quantum Gravitation, Relativity Theory Computational Mathematics and Numerical Analysis Computer science - Mathematics Numerical and Computational Physics Physics
Classificazione	530.1 - Teorie della fisica e fisica matematica
Lingua	Inglese
Numeri	ISBN: 978-3-642-24525-1 DOI: 10.1007/978-3-642-24525-1 N. catalogo straniero: QC1-999 (Library of Congress Call Number)
ID scheda	129937
Permalink	https://www.opac.inaf.it/?ids=129937