General Relativity Notes
by Edmund Bertschinger
Publisher: MIT 1999
Number of pages: 156
Working with GR, particularly with the Einstein field equations, requires some understanding of differential geometry. In this text we will develop the essential mathematics needed to describe physics in curved spacetime. These notes assume familiarity with special relativity.
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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.
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 Sergei Winitzki - Google Sites
Topics include: Asymptotic structure of spacetime, conformal diagrams, null surfaces, Raychaudhury equation, black holes, the holographic principle, singularity theorems, Einstein-Hilbert action, energy-momentum tensor, Noether's theorem, etc.
by Eric Gourgoulhon - arXiv
These notes introduce the theory of rotating stars in general relativity. The focus is on the theoretical foundations, with a detailed discussion of the spacetime symmetries, the choice of coordinates and the derivation of the equations of structure.