000 03787nam a22004935i 4500
001 978-3-642-24525-1
003 DE-He213
005 20140220083303.0
007 cr nn 008mamaa
008 120227s2012 gw | s |||| 0|eng d
020 _a9783642245251
_9978-3-642-24525-1
024 7 _a10.1007/978-3-642-24525-1
_2doi
050 4 _aQC1-999
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
082 0 4 _a530.1
_223
100 1 _aGourgoulhon, Eric.
_eauthor.
245 1 0 _a3+1 Formalism in General Relativity
_h[electronic resource] :
_bBases of Numerical Relativity /
_cby Eric Gourgoulhon.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2012.
300 _aXVII, 294p. 29 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Physics,
_x0075-8450 ;
_v846
505 0 _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.
520 _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.
650 0 _aPhysics.
650 0 _aComputer science
_xMathematics.
650 0 _aAstronomy.
650 1 4 _aPhysics.
650 2 4 _aNumerical and Computational Physics.
650 2 4 _aClassical and Quantum Gravitation, Relativity Theory.
650 2 4 _aAstronomy, Astrophysics and Cosmology.
650 2 4 _aComputational Mathematics and Numerical Analysis.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642245244
830 0 _aLecture Notes in Physics,
_x0075-8450 ;
_v846
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-24525-1
912 _aZDB-2-PHA
912 _aZDB-2-LNP
999 _c102296
_d102296