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100   $a20120227d2012      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$a3+1 Formalism in General Relativity$b[electronic resource] $eBases of Numerical Relativity /$fby Éric Gourgoulhon
205   $a1st ed. 2012.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2012.
215   $a1 online resource (XVII, 294 p. 29 illus.) 
225 1 $aLecture Notes in Physics,$x0075-8450 ;$v846
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-642-24524-2 
320   $aIncludes bibliographical references and index.
327   $aBasic 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.
330   $aThis graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in space-time, foliation of space-time by a family of space-like hypersurfaces), and then turns to the 3+1 decomposition of the Einstein equations, giving rise to the Cauchy problem with constraints, which constitutes the core of 3+1 formalism. The ADM Hamiltonian formulation of general relativity is also introduced at this stage. Finally, the decomposition of the matter and electromagnetic field equations is presented, focusing on the astrophysically relevant cases of a perfect fluid and a perfect conductor (ideal magnetohydrodynamics). The second part of the book introduces more advanced topics: the conformal transformation of the 3-metric on each hypersurface and the corresponding rewriting of the 3+1 Einstein equations, the Isenberg-Wilson-Mathews approximation to general relativity, global quantities associated with asymptotic flatness (ADM mass, linear and angular momentum) and with symmetries (Komar mass and angular momentum). In the last part, the initial data problem is studied, the choice of spacetime coordinates within the 3+1 framework is discussed and various schemes for the time integration of the 3+1 Einstein equations are reviewed. The prerequisites are those of a basic general relativity course with calculations and derivations presented in detail, making this text complete and self-contained. Numerical techniques are not covered in this book.
410  0$aLecture Notes in Physics,$x0075-8450 ;$v846
606   $aPhysics
606   $aGravitation
606   $aAstronomy
606   $aAstrophysics
606   $aComputer mathematics
606   $aNumerical and Computational Physics, Simulation$3https://scigraph.springernature.com/ontologies/product-market-codes/P19021
606   $aClassical and Quantum Gravitation, Relativity Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P19070
606   $aAstronomy, Astrophysics and Cosmology$3https://scigraph.springernature.com/ontologies/product-market-codes/P22006
606   $aComputational Mathematics and Numerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M1400X
615  0$aPhysics.
615  0$aGravitation.
615  0$aAstronomy.
615  0$aAstrophysics.
615  0$aComputer mathematics.
615 14$aNumerical and Computational Physics, Simulation.
615 24$aClassical and Quantum Gravitation, Relativity Theory.
615 24$aAstronomy, Astrophysics and Cosmology.
615 24$aComputational Mathematics and Numerical Analysis.
676   $a530.11
700   $aGourgoulhon$b Éric$4aut$4http://id.loc.gov/vocabulary/relators/aut$0953473
906   $aBOOK
912   $a996466688103316
996   $a3+1 Formalism in General Relativity$92510493
997   $aUNISA