General Relativity

This page contains the lecture notes for a 10-lecture, honours level, course on General Relativity. The course consists of a modern introduction to differential geometry, an introduction to the definitions of force and momentum in spacetime, leading up to the introduction and justification of Einstein's equations.

This page is – please use this persistent URL when citing it.

Public version 1.1, June 2013.


The distributed lecture notes.
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These notes cover, in some detail, a 10-lecture course on General Relativity, for the Honours Astronomy class, which I have delivered biennially from sessions 2002-03 to 2012-13. In the spirit of MIT’s Open Courseware, and using the licence promoted by the Creative Commons, I’m making them publicly available here. See the licence below.

This course is one of the Year B options in the Astronomy Honours course offered by the Department of Physics and Astronomy in the University of Glasgow.


The four blocks in the course are

Part 1: Introduction
What is the problem which GR attempts to solve? How does it approach the problem? [one lecture]
Part 2: Vectors, tensors and functions
A review of linear algebra, and an introduction to tensors and components [two or three lectures]
Part 3: Manifolds, vectors and differentiation
The business -- differential geometry. [four lectures]
Part 4: Physics: energy, momentum and Einstein’s equations
Back to physics. [two or three lectures]

The other resources associated with the course – longer tutorial problems, solutions, worked examples, and the like – I don’t plan to distribute outside Glasgow University. If you’re within, however, you can get to those at the course page.

warning symbolThe ‘dangerous bend’ symbol introducing certain paragraphs is intended to indicate passages you might want to skip on a first reading. They typically contain technical detail for the curious reader, or subtle points which are interesting but which might distract from the flow of the arguments, or even alternative ways of thinking about the material around them. Think of them as extended footnotes.

I am distributing these notes as PDF files: you should be able to read and print these out without difficulty, but if you have any trouble, mail me and let me know. To view and print out the PDF files, you need some program which can read them. You may already have a copy of Adobe Reader installed on your machine (or some other application which can read PDF files, such as the MacOS X Preview application); if not, you can you can download the reader free from Adobe

The PDF files below are intended to be printed out on a double-sided printer, but should look OK if printed out single-sided. The links marked ‘us’ are formatted for US ‘letter’ paper (the rest are standard A4, of course). The links in the ‘screen’ column are versions intended to be read on-screen.

Print Screen
Part 1: introduction pdf/us pdf
Part 2: vectors, tensors and functions pdf/us pdf
Part 3: manifolds, vectors and differentiation pdf/us pdf
Part 4: physics pdf/us pdf
Notation pdf/us pdf

Copyright and licence

These notes are Copyright, 2002-13, Norman Gray.

These notes are made available under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence.

Creative Commons License

Norman Gray