# NFYA04022U General Relativity and Cosmology

MSc Programme in Physics

MSc Programme in Physics with minor subject

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.

**Skills**

- 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.

**Knowledge**

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.
**Competences**

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

Academic qualifications equivalent to a BSc degree is recommended.

- Category
- Hours
- Lectures
- 35
- Preparation
- 149,5
- Practical exercises
- 21
- Exam
- 0,5
- Total
- 206,0

- Credit
- 7,5 ECTS
- Type of assessment
- Oral examination, 25 minNo preparation time.
- Exam registration requirements
It 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.

- Aid
- 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
- Re-exam
Same 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.

##### Criteria for exam assesment

see learning outcome

### Course information

- Language
- English
- Course code
- NFYA04022U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 1
- Schedule
- C
- Course capacity
- No restriction
- Course is also available as continuing and professional education
- Study board
- Study Board of Physics, Chemistry and Nanoscience

##### Contracting department

- The Niels Bohr Institute

##### Contracting faculty

- Faculty of Science

##### Course Coordinators

- Troels Harmark (7-6b64757064756e4371656c316e7831676e)