LEADER 05558nam 2200685Ia 450 001 9910465797503321 005 20200520144314.0 010 $a1-281-99870-2 010 $a9786611998707 010 $a0-19-155226-7 035 $a(CKB)2560000000296363 035 $a(EBL)430731 035 $a(OCoLC)317496332 035 $a(SSID)ssj0000087057 035 $a(PQKBManifestationID)11121225 035 $a(PQKBTitleCode)TC0000087057 035 $a(PQKBWorkID)10052113 035 $a(PQKB)10143034 035 $a(StDuBDS)EDZ0000073165 035 $a(MiAaPQ)EBC430731 035 $a(Au-PeEL)EBL430731 035 $a(CaPaEBR)ebr10288409 035 $a(CaONFJC)MIL199870 035 $a(EXLCZ)992560000000296363 100 $a20080304d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGeneral relativity and the Einstein equations$b[electronic resource] /$fYvonne Choquet-Bruhat 210 $aOxford ;$aNew York $cOxford University Press$d2009 215 $a1 online resource (812 p.) 225 1 $aOxford mathematical monographs 300 $aDescription based upon print version of record. 311 $a0-19-923072-2 311 $a0-19-171087-3 320 $aIncludes bibliographical references (p. [771]-779) and index. 327 $aCONTENTS; I: Lorentz geometry; 1 Introduction; 2 Manifolds; 3 Differentiable mappings; 4 Vectors and tensors; 4.1 Tangent and cotangent space; 4.2 Vector fields; 4.3 Tensors and tensor fields; 5 Pseudo-Riemannian metrics; 5.1 General properties; 5.2 Riemannian and Lorentzian metrics; 6 Riemannian connection; 7 Geodesics; 8 Curvature; 9 Geodesic deviation; 10 Maximum of length and conjugate points; 11 Linearized Ricci and Einstein tensors; 12 Second derivative of the Ricci tensor; II: Special Relativity; 1 Newton's mechanics; 1.1 The Galileo-Newton spacetime 327 $a1.2 Newton's dynamics - the Galileo group2 Maxwell's equations; 3 Minkowski spacetime; 3.1 Definition; 3.2 Maxwell's equations on M[sub(4)]; 4 Poincare? group; 5 Lorentz group; 5.1 General formulae; 5.2 Transformation of electric and magnetic vector fields (case n = 3); 5.3 Lorentz contraction and dilatation; 6 Special Relativity; 6.1 Proper time; 6.2 Proper frame and relative velocities; 7 Dynamics of a pointlike mass; 7.1 Newtonian law; 7.2 Relativistic law; 7.3 Equivalence of mass and energy; 8 Continuous matter; 8.1 Case of dust (incoherent matter); 8.2 Perfect fluids 327 $aIII: General relativity and Einstein's equations1 Introduction; 2 Newton's gravity law; 3 General relativity; 3.1 Physical motivations; 4 Observations and experiments; 4.1 Deviation of light rays; 4.2 Proper time, gravitational time delay; 5 Einstein's equations; 5.1 Vacuum case; 5.2 Equations with sources; 6 Field sources; 6.1 Electromagnetic sources; 6.2 Electromagnetic potential; 6.3 Yang-Mills fields; 6.4 Scalar fields; 6.5 Wave maps; 6.6 Energy conditions; 7 Lagrangians; 7.1 Einstein-Hilbert Lagrangian; 7.2 Lagrangians and stress energy tensors of sources; 7.3 Coupled Lagrangian 327 $a8 Fluid sources9 Einsteinian spacetimes; 9.1 Definition; 9.2 Regularity hypotheses; 10 Newtonian approximation; 10.1 Equations for potentials; 10.2 Equations of motion; 11 Gravitational waves; 11.1 Minkowskian approximation; 11.2 General linear waves; 12 High-frequency gravitational waves; 12.1 Phase and polarizations; 12.2 Radiative coordinates; 12.3 Energy conservation; 13 Coupled electromagnetic and gravitational waves; 13.1 Phase and polarizations; 13.2 Propagation equations; IV: Schwarzschild spacetime and black holes; 1 Introduction; 2 Spherically symmetric spacetimes 327 $a3 Schwarzschild metric4 Other coordinates; 4.1 Isotropic coordinates; 4.2 Wave coordinates; 4.3 Painleve?-Gullstrand-like coordinates; 4.4 Regge-Wheeler coordinates; 5 Schwarzschild spacetime; 6 The motion of the planets and perihelion precession; 6.1 Equations; 6.2 Results of observations; 6.3 Escape velocity; 7 Stability of circular orbits; 8 Deflection of light rays; 8.1 Theoretical prediction; 8.2 Results of observation; 8.3 Fermat's principle and light travel parameter time; 9 Red shift and time delay; 10 Spherically symmetric interior solutions; 10.1 Static solutions. Upper limit on mass 327 $a10.2 Matching with an exterior solution 330 $aAimed at researchers in mathematics and physics, this monograph, in which the author overviews the basic ideas in General Relativity, introduces the necessary mathematics and discusses some of the key open questions in the field. - ;General Relativity has passed all experimental and observational tests to model the motion of isolated bodies with strong gravitational fields, though the mathematical and numerical study of these motions is still in its infancy. It is believed that General Relativity models our cosmos, with a manifold of dimensions possibly greater than four and debatable topology 410 0$aOxford mathematical monographs. 606 $aGeneral relativity (Physics)$xMathematics 606 $aEinstein field equations 608 $aElectronic books. 615 0$aGeneral relativity (Physics)$xMathematics. 615 0$aEinstein field equations. 676 $a530.11 700 $aChoquet-Bruhat$b Yvonne$0319747 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910465797503321 996 $aGeneral relativity and the Einstein equations$9803234 997 $aUNINA