Introduction to General Relativity |
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antisymmetric tensor arbitrary Chap Christoffel symbols classical coefficients components consider const constant coordinate system corresponding covariant derivative curve defined definition density differential equations discussed do² ds² Einstein Einstein equations electromagnetic energy energy-momentum tensor equations of motion Euclidean expression field equations formula four-dimensional function galaxies geodesic geometry gravitational field hypersurface identity indices integral invariant Kerr metric line element linear Lorentz metric mathematical matrix Maxwell's equations metric tensor null observer obtain parameter particle physical plane potential problem proper-time quantity radial radius red shift relation relativistic relativity theory result Riemann space Riemann tensor Robertson-Walker metric rotating scalar Schwarzschild metric Schwarzschild solution sin² space-time special relativity stars surface symmetric tensor of rank theorem tion trajectory transformation variational vector field velocity Weyl write zero α α