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
