# FYS4160 – The General Theory of Relativity

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## Changes in the course due to coronavirus

Autumn 2020 we plan for teaching and examinations to be conducted as described in the course description and on semester pages. However, changes may occur due to the corona situation. You will receive notifications about any changes at the semester page and/or in Canvas.

Spring 2020: Teaching and examinations was digitilized. See changes and common guidelines for exams at the MN faculty spring 2020.

## Course content

The course provides a comprehensive introduction to the general theory of relativity where all forms of gravity can be described as a pure geometric effect where the curvature of space and time follows the distribution of energy and the amount momentum the matter has. An overview is given of the classical tests of  theory, and how the theory is used to describe black holes, gravitational waves and the cosmological evolution of the universe. The course also provides an introduction to differential geometry, which is necessary to be able to both formulate and apply the theory.

## 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.

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## Teaching

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) which the students prepare at home and present in the group lecture.

Regulations for mandatory assignments can be found here.

## Examination

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.

### Language of examination

The examination text is given in English. You may answer in Norwegian, Swedish, Danish or English.

### Resit an examination

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

### Special examination arrangements, use of sources, explanations and appeals

See more about examinations at UiO

Last updated from FS (Common Student System) Sep. 22, 2020 8:11:34 PM

Credits
10
Level
Master
Teaching
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.

Examination
Spring
Teaching language
Norwegian (English on request)

## Contact

Department of Physics