**Aim**

Einstein formulated the theory of general relativity as a theory for gravity in 1915. It has been verified with increasing precision during the years, and is established as the actual theory for gravitation. It gives a model for the development of the universe and gives a host of fascinating predictions. During the last century, many of them have been verified, eg. the background radiation and black holes. There is now a quite clear understanding of the principles behind the development of the universe.

The course gives a description of the theory of general relativity, starting from the equivalence principle.

The aims of the course are:

- To give an understanding and a working knowledge of the mathematics of curved spaces and space-times.

- To give an understanding and a working knowledge of how the presence of matter and energy affects the geometry of space-time.

- To use tensors for general coordinate invariance to reach Einstein's equations for the gravitational field.

- To study and deal with gravitational radiation, black holes, symmetric spaces and stan-dard models for cosmology.

- To provide a basis for further theoretical studies.

**Learning outcome (after completion of this course, the student should be able to) **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.

**Content**

History, special relativity, the equivalence principle, gravitational forces, general covariance, tensor analysis, gravitational effects in particle mechanics and electrodynamics, curvature, Einstein's field equations, the Schwarzschild solution, black holes, gravitational radiation, symmetric spaces, cosmography, standard model for cosmology, the development of the universe.

**Grades**

The grades are Fail (U), Pass (G) and Excellent (VG).

**Examination**

Home assignments, home examination, oral examination