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3+1 Formalism in General Relativity [[electronic resource] ] : Bases of Numerical Relativity / / by Éric Gourgoulhon



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Autore: Gourgoulhon Éric Visualizza persona
Titolo: 3+1 Formalism in General Relativity [[electronic resource] ] : Bases of Numerical Relativity / / by Éric Gourgoulhon Visualizza cluster
Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2012
Edizione: 1st ed. 2012.
Descrizione fisica: 1 online resource (XVII, 294 p. 29 illus.)
Disciplina: 530.11
Soggetto topico: Physics
Gravitation
Astronomy
Astrophysics
Computer mathematics
Numerical and Computational Physics, Simulation
Classical and Quantum Gravitation, Relativity Theory
Astronomy, Astrophysics and Cosmology
Computational Mathematics and Numerical Analysis
Note generali: Bibliographic Level Mode of Issuance: Monograph
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: 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.
Sommario/riassunto: 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.
Titolo autorizzato: 3+1 Formalism in General Relativity  Visualizza cluster
ISBN: 3-642-24525-0
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 996466688103316
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Serie: Lecture Notes in Physics, . 0075-8450 ; ; 846