After successful completion of the course, students are able to understand the basic concepts of black hole formation and the very notion of a black hole itself. The will have learned basic concepts of differential geometry that allow them to calculate the motion of test particles in black hole backgrounds (and as spin-off also verify the classical tests of general relativity) and the Riemann curvature tensor. They will be able to derive Einstein's equation and solve them in simple, highly symmetric, cases.

History of black holes Phenomenology of and experiments with black holes Gravitational collapse and Chandrasekhar limit Metric and geodesic equation Geodesics for Schwarzschild black holes Curvature and basics of differential geometry Hilbert action and Einstein equations Spherically symmetric black holes and Birkhoff theorem Rotating black holes: the Kerr solution Geodesics for Kerr black holes Accretion disks and black hole observations Black hole analogs in condensed matter physics Critial collapse, quasinormal modes and numerical relativity

good knowledge of special relativity is required basic knowledge of general relativity is helpful, but not required no prior knowledge of astrophysics, particle physics or cosmology is required