General Relativity

General relativity is one of the towering achievements of modern physics, the best answer we currently have to the question 'what is gravity?'. Here is where you get to grips with it - the maths can be a bit gory, but by the end you should understand the Einstein equations! These enable us to describe how mass/energy curves spacetime, which gives rise to the effects we used to call 'gravity'! After each lecture I will link material to this page - so keep checking to see what is here (and hit reload to make sure you are getting the most up to date version!). These lecture notes are NOT a substitute for attending the lectures. But do look at them because I sometimes edit them AFTER the lecture, so I emphasise and try to find other ways of explaining any points which were obviously an issue in the lecture.

WATCH the lecture timetable - I've rearranged quite a few!!

There is a highly recommended web sit of Sean Carroll's lecture notes on general relativity. I especially like his No-Nonsense Introduction to General Relativity. Only thing to watch is that he uses the opposite sign convention on his metric! His links are worth checking out as well. A very different approach (much more along the pure mathematics, differential geometry line) is an Introduction to Differential Geometry and General Relativity. But its got some good pictures in it. And an excellent essay on fundamental meaning of GR (and quantum mechanics)

I once did an experimental DU astrosoc talk on Black holes - this was midway between a lecture and my usual 'edutainment' approach to public talks.

There are also some fun relativity pages on the web
Popular science (non technical sites) include spacetime wrinkles. There are also some good visualisation sites like falling into a black hole and a make your own orbits around a black hole (java applet site).

And of course, the best yet test of Einstein in the strong field limit, the detection of gravitational waves from merging black holes!

Lecture 1:
gravity=curvature slides
and notes
Lecture 2:
Lecture 3:
Metric tensor
Lecture 4:
Covariant basis vectors and tensor summary
Lecture 5:
Derivatives in curved space
Lecture 6:
Christoffel symbols and geodesics
Lecture 7:
Geodesics and the Euler-Lagrange equations
Lecture 8:
Summary of Tensor derivatives
Lecture 9:
The Riemann Curvature Tensor
Lecture 10:
Stress-Energy tensor
Lecture 11:
The Einstein equations
Lecture 12:
The Schwarzchild metric
Lecture 13:
Weak field tests of GR
Lecture 14:
Orbits in strong gravity
and slides
Lecture 15:
Space and time round black holes
Lecture 16:
Nature of event horizon

Lecture 17:
Falling into a black hole

some figures
explore more here (including some movies)
Lecture 18:
Your questions
different coordinate transformations
science of interstellar
more on the river analogy for the event horizon, and spinning black holes
Revision lecture notes:
Revision lecture video: