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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by J.W. van Holten - arXiv
General relativity is outlined as the classical field theory of gravity, emphasizing physical phenomena rather than mathematical formalism. Dynamical solutions representing traveling waves and stationary fields of black holes are discussed.
by Gerard 't Hooft - Rinton Press
The book presents the general relativity as a scheme for describing the gravitational field and the equations it obeys. Starting from physical motivations, curved coordinates are introduced, and then the notion of an affine connection field is added.
by Eric Poisson - University of Guelph
From the table of contents: Preliminaries; Integration techniques; First post-Minkowskian approximation; Second post-Minkowskian approximation; Equations of motion; Gravitational waves; Energy radiated and radiation reaction.
by Jose Natario - Springer
This book was written as a guide for a one week course aimed at exceptional students in their final years of secondary education. The course was intended to provide a quick but nontrivial introduction to Einstein's general theory of relativity.