Waner S. Introduction to Differential Geometry and General Relativity

Hofstra University, 2002. — 128 pages. OCRPreliminaries: 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: 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, by Gregory C. Levine