The material that follows below has been retained unaltered from the previous version of the course, as it continues to form a very useful repository of material and information. I will be as happy to answer questions or provide assistance with any of these problems as with those that accompany my own lecture notes. Please do bear in mind, however, that the previous lecturer had different notational conventions than myself. [Gareth Alexander, 30th September 2015]
Problem solving is as essential in GR as in any other branch of physics. I regard it of equal importance to attending the lectures. 150 hours of your effort is associated with this 15-CAT course. Allowing for lectures, 120 hours covers reading, problems and revision, i.e. 12 hours/week. Try to set aside 7 hours/week for tackling the problems ... some chance, I know, but do your best.
Some of the problems here involve heavy algebra which I would not give in an examination. In some cases these fill in gaps from lectures where a long derivation would be a waste of time. They are nonetheless useful for practicing the index manipulations so characteristic of GR and to build your confidence.
Solutions will become available after an appropriate period of time. Hints and Answers will be available later in the term, but they are kept separate to encourage you first to try without the hints.
Please have a go at these! If you have tried but failed, then take a look at the hints, and have another go. Only after this look at the model answers. Making the effort to crack a problem, even if you fail, is valuable. Given that problem sheets are "open book", many of the problems here lack the guidance you would be given in an exam (e.g. I don't expect you to be able to recall the formulae for the Levi-Civita connection or curvature tensor in an exam but regard the process of looking them up in a book to be useful); you should expect to refer to your notes and books to solve many of them. Don't be discouraged if you can't do them at first: you can't get good at playing a musical instrument without practice, and its the same with physics, so, like a terrier, just keep at it!
Note - these were revised for 2013/14 and remain valid in 2014/15.
Problems (PDF file) -- all.