The Geometry of General Relativity
by Tevian Dray
Publisher: Oregon State University 2014
Number of pages: 158
The manuscript emphasizes the use of differential forms, rather than tensors, which are barely mentioned. The focus is on the basic examples, namely the Schwarzschild black hole and the Friedmann-Robertson-Walker cosmological models. The material should be suitable for both advanced undergraduates and beginning graduate students in both mathematics and physics.
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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 Joseph C. Kolecki - Glenn Research Center
Tensor analysis is useful because of its great generality and compact notation. This monograph provides a conceptual foundation for students of physics and engineering who wish to pursue tensor analysis as part of their advanced studies.
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 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.