Partial Differential Equations of Physics
by Robert Geroch
Publisher: arXiv 1996
Number of pages: 57
All partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form. We describe some broad features of systems of differential equations so formulated. Examples of such features include hyperbolicity of the equations, constraints and their roles, how diffeomorphism freedom is manifest, and how interactions between systems arise and operate.
Home page url
Download or read it online for free here:
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 Shlomo Sternberg
Course notes for an introduction to Riemannian geometry and its principal physical application, Einstein’s theory of general relativity. The background assumed is a good grounding in linear algebra and in advanced calculus.
by Arthur Stanley Eddington - Cambridge University Press
The author gives an account of general relativity theory without introducing anything very technical in the way of mathematics, physics, or philosophy. It is hoped that the book may also appeal to those who have gone into the subject more deeply.
by Giampiero Esposito - arXiv
An attempt is made of giving a self-contained introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, spinor and twistor methods, heaven spaces.