Waner S. Introduction to Differential Geometry and General Relativity

Hofstra University, 2002. — 128 pages.Premilinaries: Distance, Open set, Parametric Surfaces and Smooth Functions; Smooth Manifolds and Scalar Fields; Tangeut Vectors and Taugent Space; Contravariant and Covariant Vector Fields; Tensor Fields; Rienannian Manifolds; Locally Minkowskian Manifolds: An Introduction to Relativity; Covariant Differentiation; Geodesics and Local Inertial Frames; The Riemann Curvature Tensor; A Little More Relativity: Comoving Frames and Proper Time; The Stress Tensor and the Relativistic Stress-Energy Tensor; Two 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.