Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

General Relativity and Cosmology

Practical information
Study year 2016/2017
Block 1
Programme level Full Degree Master
Course responsible
  • Troels Harmark (7-70697a75697a7348766a7136737d366c73)
  • The Niels Bohr Institute
Course number: NFYA04022U

Course content

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.



Recommended prerequisites

Classical mechanics, special relativity. Analytical mechanics may be useful, but is not necessary

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M.Sc. Physics


Study Board of Physics, Chemistry and Nanoscience

Course type

Single subject courses (day)


1 block


---- SKEMA LINK ----

Teaching and learning methods

Lectures and theoretical exercises


No restricion to number of participants




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://www.nbi.dk/~polesen/)


Category Hours
Lectures 28
Practical exercises 28
Exam 0,5
Preparation 149,5
English 206,0


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

Criteria for exam assessment

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.

Censorship form

No external censorship
More internal examiners
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