General Relativity 1100-GR

1. Euclidean and Minkowski spaces:
affine spaces, affine spaces equipped with a scalar product.

2. Basics of differential geometry:
tensor calculus, differentiable manifolds, tensor fields, metrics, Lie derivative, covariant derivative, Riemann tensor, parallel transport, Killing vector fields.

3. Formulation of General Relativity:
basic concepts, postulates of GR, Einstein's equation.

4. Weak gravitational fields:
linearized Einstein's equation, Newtonian limit of GR, linear gravitational waves.

5. Schwarzschild spacetime:
static spherically symmetric spacetime, Schwarzschild metric, free test particles in the Schwarzschild spacetime, Kruskal-Szekeres extention, Schwarzschild black hole.

6. The simplest cosmological models
spatially homogeneous and isotropic spacetime, Robertson-Walker metrics, models with dust and radiation, Hubble law