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General Relativity and Cosmology - PhD Course
Provider: Faculty of Science

Activity no.: 5864-21-11-32
Enrollment deadline: 06/08/2021
Date and time06.09.2021, at: 09:00 - 12.11.2021, at: 16:00
Regular seats20
ECTS credits7.50
Contact personJulie Meier Hansen    E-mail address: juliemh@nbi.ku.dk
Enrolment Handling/Course OrganiserTroels Harmark    E-mail address: harmark@nbi.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 1
Scheme groupC
Exam requirementsIt is mandatory to take all the given 3 quizzes during the course. It is not required to pass the quizzes and the quizzes are not part of the exam evaluation.
Exam formOral examination, 25 min
Exam detailsNo preparation time. Aid: One "A4" piece of paper with the students notes.
Exam aidsOnly certain aids allowed
Grading scalePassed / Not passed
Censorship formNo external censorship More internal examiners
Exam re-examinationSame as regular exam. Students who have not taken the quizzes during the course, should do so in Absalon at least 3 weeks before the re-exam. If you do not have access to the latest Absalon room, please contact the course responsible.
Course workload
Course workload categoryHours
Practical exercises21.00


The purpose of this course is that the student obtains a basic understanding of general relativity and its applications.
The first part of the course gives an introduction to Einstein's theory of general relativity. The second part of the course gives an introduction to its applications to planetary motion, bending of light, black holes, gravitational waves and cosmology.

Learning outcome


  • When the course is finished it is expected that the student is able to explain Einsteins equivalence principle, explain how this leads to introducing a general metric for space-time, and describe the physical and mathematical meaning of geodesic motion.
  • The student should be able to apply the principle of general covariance along with the mathematical tools of tensors and covariant derivatives to formulate laws of nature.
  • The student should understand the notion of curvature of space-time and explain 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, describe the geodesics in this geometry and apply this to planetary orbits in the solar system and the bending of light around massive objects.
  • The student should be able to show how the Schwarzschild solution gives rise to the notion of black holes.
  • The student should be able to interpret the Kerr metric as a rotating black hole.
  • The student should be able to explain what a gravitational wave is and how it affects the relative motion of test particles.
  • Finally, the student should be able to explain the basic ingredients of cosmology as derived in the framework of general relativity, 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 Einsteins equivalence principle, the concept of general covariance, geodesic motion and the Einstein equations. As applications we will discuss the Schwarzschild solution and its geodesics, black holes, gravitational waves 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.

See Absalon for final course material. The following is an example of expected course litterature.

Lecture notes by Troels Harmark

Target group

This course is offered to MSc and PhD students. Complete course description and sign-up for MSc students >> here.

PhD students please see below for information on signing up.


Teaching and learning methods
Lectures and theoretical exercises.

Recommended Academic Qualifications:

The mandatory courses on first and second year of the bachelor (particularly the courses covering classical mechanics, special relativity, mathematical methods, electromagnetism). Analytical mechanics is not a necessary prerequisite.

Academic qualifications equivalent to a BSc degree is recommended.

Applying for the course:

PhD students: Please sign up for the course using the credit student application at this link

The course code to enter is NFYA04022U 

Please contact Julie Meier Hansen if you have any questions or problems with signing up. 

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