After successful completion of the course, students are able to are in postion to reproduce the  contnts as outlined in detail in the english version of "Lehrinhalte" in written as well as oral form. Moreover the students will be able to apply the basic concepts of  Geometrie und Gravitation I to simple examples.

1 Kruskal-extension of Schwarzschild, Conformal compactification, Penrose diagrams 2 Geometry of null-congruences, Sachs equations, Rotating black holes, Kerr geometry 3 Gaussian coordinates, ADM decomposition, Extrinsic curvature and initial value problem, Hamiltonian formulation 4 Cosmological principle, Homogeneity and Isotropy, Fiedmann-Robertson-Walker Geometries, Hubble's law and scalefactor 5 Variational principle, Einstein-Hilbert action and Hawking-boundary term, Concepts from Euclidean Quantum Gravity, Hawking temperature

lecture with a strong and active student participation.

oral exam