NFYA04022U General Relativity and Cosmology

Volume 2013/2014
MSc Programme in Physics
The purpose of this course is that the student obtains a basic understanding of general relativity and cosmology, and becomes able to apply this to elementary phenomena.

This course gives an introduction to Einstein's general relativity, including a number of exact solutions. Black holes are discussed. The second part of the course gives an introduction to cosmology.
Learning Outcome

  • When the course is finished it is expected that the student is able to explain the equivalence principle and describe the physical and mathematical meaning of geodesic motion.
  • The student should understand the principle of general covariance and how this can be used to arrive at the Einstein equations.
  • The student should be able to derive the Schwarzschild geometry around a static and spherically symmetric distribution of matter and describe the geodesics in this geometry along with the connection to experimental tests.
  • The student should be able to show how the Schwarzschild solution gives rise to the notion of black holes and understand the Kruskal extension.
  • Finally, the student should be able to explain the basic ingredients of cosmology, including the evolution of the scale factor of the universe given different energy momentum components.
The course introduces the student to the concept of gravity as a property of the geometry of spacetime itself, leading to Einstein's theory of general relativity. This includes the Einstein equivalence principle, the concept of general covariance, geodesic motion and the Einstein equations. As applications we will discuss the Schwarzschild solution and its geodesics, experimental tests, black holes and cosmology.

This course makes use of previously obtained knowledge in
Newtonian mechanics, special relativity and vector calculus
as well other related fields such as astrophysics and particle physics. After the course, the student should have a better picture of how general relativity fits into the latter subjects. Furthermore, the course is a good preparation for other more advanced courses in for example cosmology, high-energy physics and string theory.
Spacetime and Geometry: An Introduction to General Relativity, Sean Carroll (Addison-Wesley) (further recommend are Notes (Autumn 2007, ps file) which can be found on the net at the address: http:/​/​​~polesen/​)
Classical mechanics, special relativity
Lectures and theoretical exercises
  • Category
  • Hours
  • Exam
  • 0,5
  • Lectures
  • 28
  • Practical exercises
  • 28
  • Preparation
  • 149,5
  • Total
  • 206,0
7,5 ECTS
Type of assessment
Oral examination, 25 min
No preparation time.
Only certain aids allowed
One "A4" piece of paper with the students notes.
Marking scale
7-point grading scale
Censorship form
No external censorship
More internal examiners
Criteria for exam assesment

12 for an excellent performance displaying a high level of command of all aspects of the relevant material, with no or only a few minor weaknesses.