Astronomy Honours: General Relativity and Gravitation I

Session 2020–21

Notes and contents

The notes are availeble in the A345 moodle.

These four blocks are as follows.

Part 1: Introduction
What is the problem which GR attempts to solve? How does it approach the problem? Book list, and pointers to further reading. [one lecture]
Part 2: Vectors, tensors and functions
A review of linear algebra, and an introduction to tensors and components. [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 (ie, the point of the course). [three lectures]

These notes are intended to be self-contained. However they are also designed to be compatible with the recommended course book (Bernard F Schutz, A First Course in General Relativity. Cambridge University Press, second edition, 2009. ISBN 978-0-521-88705-2). This is also the recommended text for GRG2.

You will notice that only parts 1 and 4 have much in the way of physics! GRG1 is intended to deal with the mathematical technology that you require to understand gravity, and ends up not having much time to apply that maths to the science. That's what GRG2 is for.

dangerous-bend symbol The ‘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 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. The material in these paragraphs is not examinable.

For all lectures other than lecture 1, I will presume that you have already printed out the relevant part, and at least looked over it. You will not need to, and indeed should not expect to, understand things first time, but this preliminary scan should give you an indication of what bits of the lecture you need to pay special attention to. Having said that, don't be in a rush to print out everything – as I spot typos or other infelicities, I will occasionally adjust the notes as distributed here.

Other remarks

If anyone needs special versions of these notes (with large print or in particular colours for example), I can surely produce those very easily – let me know.

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.

I've taught this course, in alternate years, since about 2000. This resulted in a book, derived from these notes, which was published by CUP in 2019.

Norman Gray
2021 April 6