Astronomy Honours: General Relativity and Gravitation I

Session 2018–19


I'm making available audio versions of the lectures.
The distributed lecture notes. Aims and objectives.
All exercises
All the exercises, with selected solutions.
What's new
Recent changes to this page (see also the updates RSS feed)

Podcast icon for RSS feed

I make available audio versions of the lectures, that is, a podcast. Please do let me know how you get on. I'm interested in whether you use these recordings, how, when, why, where, plus any other feedback that occurs to you.

If you have any problems with the feed, or with the enclosed MP3 files, do let me know fairly urgently.

Notes and contents

From this page you can (as the course goes on) download the notes for each of the four blocks of the General Relativity course (these are on Moodle; for a ‘public’ version, see elsewhere).

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 : notes ]
Part 2: Vectors, tensors and functions
A review of linear algebra, and an introduction to tensors and components
[ three lectures : notes ]
Part 3: Manifolds, vectors and differentiation
The business – differential geometry.
[ four lectures : notes ]
Part 4: Physics: energy, momentum and Einstein's equations
Back to physics (ie, the point of the course)
[ three lectures : notes ].

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.

Other resources

Notation crib sheet
Context matters... [ notes ]
Aims and Objectives
This is the final version of the aims and objectives for this year [ PDF ].
Quick questions
Here are the quick-questions for parts one to four [ PDF ].
The scans of the handwritten overheads are available.

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.

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.

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.

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.

All in-text questions, with answers

I've gathered together into a single document, all the exercises which appeared in the various parts of the course, at the same time amplifying or adding the notes for those exercises.

Not every single problem has an answer. Some problems lead you through themselves in sufficient detail that (I think) they don't need further notes. The questions are not necessarily in the best order, with easier ones before harder ones; I think they're about right, but on this, as well as on the problems selected for fuller answers, I'd welcome comments.

Obligatory rant: Solving problems like these is very valuable, since it forces you to think through the sometimes rather tricky material which they illustrate; sometimes, indeed, there are aspects of detail which only become clear when you try them out on a problem. However, the questions are useful only if you work through them yourself, and so the notes added here are intended only to help you when you get stuck, to allow you to check the answer you've obtained, or to add further details. There is less than no point in looking at the answers before you've attempted the question yourself. You will think `yes, that makes sense; I would have written that', and be filled with illusory confidence.

Download: on Moodle.

Questions questionnaire

The exercises included in the lecture notes are pretty various. Some are quite easy, and others hard. As payoff, some are very valuable, and others less so.

I have an idea of roughly which problems are in which category, but (a) it's not really my opinion that matters, and (b) the report that “last year's students said ‘X’” is much more interesting and valuable to next year's students than anything I can say. Can I ask you, therefore, if you could score each of the problems in the problem set. At the end of the exercises compendium, above, I've prepared a questionnaire which covers this; you're most likely to be able to answer this around revision or exam time, so if you could get this back to me around then, as paper or as a scan, that'd be great.

Recent changes

Release final version of A&O, and quick-questions
Tweak and release part4 notes
Release all-exercises+notes document
Release part3 notes, and notation reference
Adjustments to web page: include links to scanned overheads, and podcast
Release part2 notes
Norman Gray