NFYA04022U General Relativity and Cosmology

Skills

• When the course is finished it is expected that the student is able to explain the equivalence principle and describe the physical and mathematical meaning of geodesic motion.
• The student should understand the principle of general covariance and how this can be used to arrive at the Einstein equations.
• The student should be able to derive the Schwarzschild geometry around a static and spherically symmetric distribution of matter and describe the geodesics in this geometry along with the connection to experimental tests.
• The student should be able to show how the Schwarzschild solution gives rise to the notion of black holes and understand the Kruskal extension.
• Finally, the student should be able to explain the basic ingredients of cosmology, including the evolution of the scale factor of the universe given different energy momentum components.

Knowledge
The course introduces the student to the concept of gravity as a property of the geometry of spacetime itself, leading to Einstein's theory of general relativity. This includes the Einstein equivalence principle, the concept of general covariance, geodesic motion and the Einstein equations. As applications we will discuss the Schwarzschild solution and its geodesics, experimental tests, black holes and cosmology.

Competences
This course makes use of previously obtained knowledge in
Newtonian mechanics, special relativity and vector calculus
as well other related fields such as astrophysics and particle physics. After the course, the student should have a better picture of how general relativity fits into the latter subjects. Furthermore, the course is a good preparation for other more advanced courses in for example cosmology, high-energy physics and string theory.