This course is discontinued

FYS9160 – The general theory of relativity

Course content

Tensors and differential forms. Physical interpretation of the metric tensor. The geodesic equation. Einstein's field equations. Solutions of the equations. Tests of the general theory of relativity. Mercury's perihelion shift. Deflection of light. Gravitational time dilation. Black holes. Deduction of the Tolman-Oppenheimer Volkov equation for relativistic stars. Cosmology.

Learning outcome

Knowledge Objectives:

The students shall be familiar with the fundamental principles of the theory of relativity. They shall know the meaning of the concept “inertial frame” and how gravity is understood in the theory of relativity. The student shall be familiar with the fundamental concepts and main contents of the theory of relativity: The principle of relativity, the kinematic- and the gravitational time dilation and frequency shift, curved spacetime, gravitational bending of light and relativistic universe 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. The shall be familiar with covariant derivative and covariant Lagrangian dynamics, geodesic curves and Cartan’s structure equations. They shall be able to calculate the components of the Riemann curvature tensor from a given line element. They shall also be able to write down the energy-momentum tensor for a perfect fluid and solve Einstein’s field equations for static spherically symmetric problems and for isotropic and homogeneous universe models. They shall master calculating the relativistic time dilation for clocks moving in a gravitational field and be able to calculate the corresponding frequency shift for sources moving in a gravitational field. They shall also master calculating the bending of light passing a spherical mass distribution and the precession of perihelion for a planet in the Solar system. The students shall also be able to give a mathematical description of relativistic star models and universe models.


PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.

If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.

PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.


Formal prerequisite knowledge

No prerequisites.

Recommended previous knowledge

FYS3120 – Classical Mechanics and Electrodynamics.

Overlapping courses

10 credits overlap against FYS307.

10 credits with FYS4160 – The General Theory of Relativity


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


Oral exam at the end of the semester.

Grading scale

Grades are awarded on a pass/fail scale. Read more about the grading system.

Facts about this course






Last teaching semester: spring 2009.


Last exam semester: spring 2011.

Teaching language

Norwegian (English on request)