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 Sean M. Carroll - University of California
Lecture notes on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications: gravitational radiation, black holes, and cosmology.
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 Edmund Bertschinger - MIT
Working with GR 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.
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.