Spacetime and Fields
by Nikodem J. Poplawski
Publisher: arXiv 2009
Number of pages: 114
We present a self-contained introduction to the classical theory of spacetime and fields. The order of the presentation is: 1. Spacetime (tensors, affine connection, curvature, metric, tetrad and spin connection, Lorentz group, spinors), 2. Fields (principle of least action, action for gravitational field, matter, symmetries and conservation laws, gravitational field equations, spinor fields, electromagnetic field).
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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 Sean M. Carroll
General relativity has a reputation of being extremely difficult. This introduction is a very pragmatic affair, intended to give you some immediate feel for the language of GR. It does not substitute for a deep understanding -- that takes more work.
by Horst R. Beyer - arXiv
This course introduces the use of semigroup methods in the solution of linear and nonlinear (quasi-linear) hyperbolic partial differential equations, with particular application to wave equations and Hermitian hyperbolic systems.
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.