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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
FFM071 - Gravitation and cosmology
Gravitation och kosmologi
Syllabus adopted 2019-02-14 by Head of Programme (or corresponding)
Owner: MPPHS
7,5 Credits
Grading: TH - Five, Four, Three, Fail
Education cycle: Second-cycle
Major subject: Engineering Physics
Department: 16 - PHYSICS

Teaching language: English
Application code: 85113
Open for exchange students: Yes
Block schedule: A

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0101 Examination 7,5 c Grading: TH   7,5 c   Contact examiner,  Contact examiner,  Contact examiner

In programs

MPPHS PHYSICS, MSC PROGR, Year 1 (compulsory elective)


Bengt E W Nilsson

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In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

Course specific prerequisites

Newtonian mechanics, linear algebra, special theory of relativity, electromagnetic field theory.


Einstein formulated the theory of general relativity as a theory for gravity in 1915. It has since then been verified with increasing precision, and is by now established as the correct theory of gravitation. The theory can be used to analyze the evolution of our universe, and has made astounding predictions of new physics, such as black holes and gravitational radiation.

The course gives an introduction to the theory of general relativity, including the mathematical formalism underlying it as well as its physical implications. The purpose of the course

is to provide the students with a working knowledge of the basic concepts of general relativity, ensuring that after completion of the course they are well equipped to take on more advanced topics, including the study of research articles in the field.

Learning outcomes (after completion of the course the student should be able to)

- understand Einstein's principle of equivalence.

- have an understanding and a working knowledge of the mathematical description of curved spaces and spacetimes.

- understand the how the presence of matter and energy affects the geometry of spacetime.

- be able to understand and use the mathematical formalism of tensors in order to describe physics in a coordinate-independent way.

- understand Einstein's equations, and describe the basic steps for how to solve them.

- be able to derive Einstein's equations from an action principle, and explain how this action principle can be used to couple the theory to other physical theories, such as electrodynamics.

- be able to study and deal with the topics of gravitational radiation, black holes, symmetric spaces and models for cosmology.

The student is expected to demonstrate, during and after the course, a knowledge of the material covered in the course, and an ability to apply advanced mathematical methods to analytical calculations and advanced problem-solving in the subject.


- Brief history of the subject.
- Basics of special relativity.
- The principle of equivalence and gravitational forces.
- Tensor analysis and the principle of general covariance.
- Gravitational effects in particle mechanics and electrodynamics.
- Curvature of spacetime.
- Einstein's field equations.
- The Schwarzschild solution and black holes.
- Gravitational radiation.
- The mathematics of symmetric spaces.
- Standard model for cosmology and the evolution of the universe.


Lectures, exercise classes.


(1) S Weinberg: Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. John Wiley & Sons Inc. 1972.
(2) Lecture Notes on General Relativity by Sean Carroll (available from the link:

Examination including compulsory elements

2 short home assignments during the course. The course will then be concluded with a longer home examination, followed by an oral examination for those students who wish to have the highest grade.

Page manager Published: Thu 04 Feb 2021.