LEADER 03873nam 2200577Ia 450 001 9910133753003321 005 20200520144314.0 010 $a3-642-24525-0 024 7 $a10.1007/978-3-642-24525-1 035 $a(CKB)3360000000365791 035 $a(SSID)ssj0000630010 035 $a(PQKBManifestationID)11941406 035 $a(PQKBTitleCode)TC0000630010 035 $a(PQKBWorkID)10744846 035 $a(PQKB)11439433 035 $a(DE-He213)978-3-642-24525-1 035 $a(MiAaPQ)EBC3070512 035 $a(PPN)159085128 035 $a(EXLCZ)993360000000365791 100 $a20111028d2012 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$a3+1 formalism in general relativity $ebases of numerical relativity /$fEric Gourgoulhon 205 $a1st ed. 2012. 210 $aBerlin ;$aHeidelberg $cSpringer$dc2012 215 $a1 online resource (XVII, 294 p. 29 illus.) 225 1 $aLecture notes in physics,$x0075-8450 ;$vv. 846 300 $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 ;$v846. 517 3 $a3 + 1 formalism in general relativity 517 3 $a3 plus 1 formalism in general relativity 606 $aGeneral relativity (Physics)$xMathematics 606 $aPhysics 615 0$aGeneral relativity (Physics)$xMathematics. 615 0$aPhysics. 676 $a530.11 700 $aGourgoulhon$b Eric$00 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910133753003321 996 $a3+1 Formalism in General Relativity$92510493 997 $aUNINA