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Syllabus for

Academic year
FFM071 - Gravitation and cosmology
Gravitation och kosmologi
Syllabus adopted 2020-02-19 by Head of Programme (or corresponding)
Owner: MPPHS
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: Second-cycle
Major subject: Engineering Physics
Department: 16 - PHYSICS

Teaching language: English
Application code: 85118
Open for exchange students: Yes
Block schedule: A

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

In programs

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


Bengt E W Nilsson

  Go to Course Homepage


General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

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


(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 at

Examination including compulsory elements

- A number of home assignments during the course (mandatory, weight 40% in final grade)

- The course is  concluded with an oral examination (mandatory, weight 60% in final grade)

Published: Mon 28 Nov 2016.