FYS4160 – The General Theory of Relativity

Schedule, syllabus and examination date

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Course content

Equivalence principles. Motion in the gravitational field. Tensors and differential forms. Riemannian Geometry. Einstein's field equations. Schwarzschild solution and black holes. Tests of the general theory of relativity. Gravitational waves. Cosmology.

Learning outcome

Knowledge Objectives:

The students shall be familiar with the fundamental principles of the general theory of relativity. They shall know the meaning of basic concepts like the equivalence principles, inertial frames and how gravity is understood as a manifestation of a curved space-time. They shall also be familiar with some of the main contents of the theory: motion in the gravitational field, time dilation and frequency shifts, bending of light, gravitational waves and cosmological models with expanding space.


Ability Objectives:

The students shall master calculating with tensors and differential forms. They shall also be able to describe physical phenomena in different coordinate systems and to transform from one coordinate system to another. They shall be familiar with covariant derivative and covariant Lagrangian dynamics, geodesic curves, and be able to calculate the components of the Riemann curvature tensor from a given line element. They shall also be able to solve Einstein’s field equations for static spherically symmetric problems and for isotropic and homogeneous cosmological models. They shall master calculating the relativistic frequency shifts for sources moving in a gravitational field, as well as the bending of light passing a spherical mass distribution. The students shall also be able to give a mathematical description of gravitational waves, as well as cosmological models in the context of general relativity.



Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.


Recommended previous knowledge

We strongly advice that you have taken the following courses:

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The course extends over one full semester having 6 hours of teaching per week (lectures and problem solving).

The course also includes homework problems (approximately one per week).

Regulations for mandatory assignments can be found here.



Oral or written exam is decided after registration depending on how many students have registered for exam. The final exam Counts 90% and the home work problems Counts 10% of the final grade.

Examination support material

3 A4 pages (two-sided) with own notes.

Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

Explanations and appeals

Resit an examination

This course offers both postponed and resit of examination. Read more:

Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.


The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

Facts about this course






Every spring

If the course is offered, a minimum of four students is required for ordinary lectures to take place. If less than four students participate, an exam will be given, but one should not expect ordinary teaching.


Every spring

Teaching language

Norwegian (English on request)