General Relativity

General Relativity

The general theory of relativity is Einstein's theory of gravity. Here he shows that gravity should not be described as a force, as in Newtonian physics, but instead as a consequence of the curvature of space and time. In short, gravity is spacetime geometry.

This course is about this remarkable discovery: what it means, how the theory can be (and has been) tested, its predictions and consequences.

Note: The reexam will be Friday August 30 2019, 8:00 – 13:00, in room FP22. (This room is located on the AlbaNova campus in the yellow building next to the bus stop Ruddammen)

Course material

(Will be updated during the course.)

Exam 2019

Here is the Exam (June 5) with solutions:

Bonustest II

Here is Bonustest II (May 16) and answers to it:

Bonustest I

Here is Bonustest I (April 15) and answers to it:

Exam 2018

Lecture notes

Please note that these notes are written primarily for myself as support during the lecture. Their content may therefore not be understandable for someone who didn't attend the lecture. (The first page is usually a summary of the content of the lecture. Green text are things that I say but not write on the board. Pink question marks are things that I may ask during the lecture).

Course content

We start by introducing the basic ideas behind the theory, such as the equivalence principle, how to describe curved spaces and spacetimes in terms of a metric, and the true importance of special relativity as a locally valid theory. Then we use this to study the most important case: the Schwarzschild spacetime, that is, the spacetime outside a spherically symmetric mass distribution such as a planet, a star or a black hole.

Only thereafter we move on to the more mathematical parts of the theory, introducing covariant derivative, the curvature tensor, the stress energy tensor and Einstein's equations.

We then discuss some interesting applications of the theory, such as black holes, cosmology and gravitational radiation.

Course literature

James B. Hartle: Gravity - an Introduction to Einstein's General Relativity (Addison Wesley 2003, ISBN: 0-8053-8662-9)

Note that the book now exists in two versions, the original one and, unfortunately, a bad new one.

This is the one you should buy:

Do NOT buy the so called "New international edition" from Pearson:

The appendices are missing, the page numbering is wrong and the paper quality is very bad. The book is essentially useless. The original book is more expensive, but it is worth it. Note that it may soon be out of stock in Europe.


The lectures are given by Sören Holst. If you have any questions concerning the course, don't hesitate to contact me at

The problem solving sessions will be led by Anders Lundkvist.

Official course plan