General Relativity

Welcome to B5 General Relativity! This term I am the tutor for B5 in St Hilda’s College and Mansfield College. This is an introductory course in general relativity, developed by Einstein over a century ago in May 1916 and lies in the foundation of modern physics. In this course you will learn, properly, what ‘relativity’ means, and how a lot of beautiful mathematics lies under this well-known theory.

There are generally two schools of thought in teaching general relativity. One is to take the operational perspective and introduce only the mathematical components, namely tensor analysis, in order to develop some physical intuition to Einstein’s equations and emphasise on the physical results. This is normally the stance taken when teaching a first course in general relativity — emphasising on the astrophysical applications and calculations and developing an intuition for the subject. The more modern version, and the one that I would really advocate for, is to teach general relativity with differential geometry in mind, and emphasise on the geometrical interpretation of the equation. This really should be (at least, in the modern perspective) how you should understand general relativity as you pursue further in the field.

But a first introduction is enough. There is still quite a lot. And whilst Andrei will emphasise a lot of these interpretations in the lectures, we will first need to be able to do the basic maths and physics and all the calculations. A very good book for this is Hobson’s General Relativity, which takes a very similar view as Prof Balbus’s version of the course (as well as the Cambridge version…). If you are stuck on the questions or basics, start here. The other good read is Weinberg’s Gravitation and Cosmology, and whilst it has a lot of drawbacks (on both geometrical interpretations and black hole applications) the cosmology part of the book is one of the best introductions anywhere in the world. The book that I will recommend is Dirac’s little monograph written by the one and only Paul Dirac — this 70 page book certainly packs a bunch and in my opinion is the best and most physical intuitive summaries of relativity you can find out there.

Some of you might want a better picture. The next step would be to do GR (and we can certainly discuss this in the tutorials) properly with differential geometry — and introduce all the concepts with manifolds, vector fields, flows… Spacetime, after all, should be intepreted as a Riemannian manifold. The canonical reference is Wald’s GR, but you might also find these Part III notes by Reall very useful. Differential geometry, of course, is a whole other deep hole we can decide to fall into…

We will stay put and work hard. It will take us far.

Details for tutorials

My tutorials will be held at either St Hilda’s or Mansfield.

For St Hilda’s, the tutorials will be organised on Tuesdays, Weeks 2,4,6,7,8. Location is TBC.

For the first tutorial we will discuss some tensor methods and some differential geometry. Finish the first sheet as far as you can but let me know if you run into problems as the sheet will cover material a bit further ahead in the lectures.

For Mansfield, I will organise the timetable for the tutorials a bit later.

For homework please send me an email titled ‘College GR Problem Sheet X’. Deadline is the day before the tutorial at noon.

Extra Materials

Tutorial 1.

(to be updated )