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.
Download or read it online for free here:
by Neil Lambert - King's College London
This course is meant as introduction to what is widely considered to be the most beautiful and imaginative physical theory ever devised: General Relativity. It is assumed that you have a reasonable knowledge of Special Relativity as well as tensors.
by Matthias Blau - Universitaet Bern
The first half of the book is dedicated to developing the machinery of tensor calculus and Riemannian geometry required to describe physics in a curved space time. We will then turn to various applications of General Relativity.
by Hermann Weyl - Methuen & Co.
A classic of physics -- the first systematic presentation of Einstein's theory of relativity. Long one of the standard texts in the field, this excellent introduction probes deeply into Einstein's general relativity, gravitational waves and energy.
by Pankaj S. Joshi, Daniele Malafarina - arXiv
The research of recent years has provided considerable clarity and insight on stellar collapse, black holes and the nature and structure of spacetime singularities. In this text, the authors discuss several of these developments here.