General Relativity

The course begins by introducing the basic ideas behind the theory, such as the equivalence principle, how to describe curved spaces in terms of a metric, and the importance of special relativity as a locally valid theory. These insights are then used to study the Schwarzschild spacetime – the spacetime outside a spherically symmetric mass distribution, such as a planet, star or black hole. Thereafter we move on to the more mathematical parts of the theory, introducing tensors, the concept of parallel transport, the covariant derivative and the Riemann curvature tensor. After a discussion of the stress energy tensor we are then able to write down Einstein's equation, describing the connection between spacetime curvature and matter. In the last part of the course we discuss some important consequences of the theory, such as black holes, cosmology and gravitational waves.