Introduction to Differential Geometry and General Relativity
by Stefan Waner
Number of pages: 138
From the table of contents: distance, open sets, parametric surfaces and smooth functions, smooth manifolds and scalar fields, tangent vectors and the tangent space, contravariant and covariant vector fields, tensor fields, Riemannian manifolds, locally Minkowskian manifolds, covariant differentiation, geodesics and local inertial frames, the Riemann curvature tensor, comoving frames and proper time, the stress tensor and the relativistic stress-energy tensor, three basic premises of general relativity, the Einstein field equations and derivation of Newton's law, the Schwarzschild metric and event horizons, White Dwarfs, neutron stars and black holes.
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