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2 The Field Equations of Gonere Relativity
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abcd absolute derivative affine parameter affinely parametrized geodesic assume assumption Bianchi identity connection independent constant contravariant vector field coordinate patches cosmological curvature curve Deduce defined density differential Einstein equations event horizon exercise field equations Figure fluid Friedman equation function fundamental observers Geodesic Deviation geodesic equation gravitational field homogeneous and isotropic hypersurfaces infinite isometry group Killing vector light cone manifold matter content Maxwell's equations metric g Newtonian null geodesics null surface orbit orthogonal parametrised geodesic particle paths radius red shift Ricci scalar Ricci tensor Riemann tensor scalar field scale factor Schwarzschild solution Show singularity solving the geodesic space-like geodesics space-time spherically symmetric star Suppose tangent vector tensor field theorem theory time-like transformation universe vacuum equations valence vanishes vector field velocity whence world lines zero