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 Benjamin Crowell - lightandmatter.com
This is an undergraduate textbook on general relativity. It is well adapted for self-study, and answers are given in the back of the book for almost all the problems. The ratio of conceptual to mathematical problems is higher than in most books.
by Christian Heinicke, Friedrich W. Hehl - arXiv
Starting from Newton's gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein's vacuum field equation, the Schwarzschild solution, and into one specific stationary solution, the Kerr solution.
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.
by J.L. Jaramillo, E. Gourgoulhon - arXiv
We present an introduction to mass and angular momentum in General Relativity. After briefly reviewing energy-momentum for matter fields, first in the flat Minkowski case (Special Relativity) and then in curved spacetimes with or without symmetries.