Notes
Course notes prepared by the instructor. At students' request I have scanned my lecture notes. Be advised that they are written for my own use, so they tend to have scratches and corrections and marginal notes that may be irrelevant! If anyone wants to transfer them to LaTeX please get in touch with the instructor.
You may also want to use your favorite search engine to look for General Relativity Lecture Notes.
For example, you can find there Notes by Sean Carroll and by Sergei Winitzki.
Chapter 1: Mathematical review
Review of elements of differential geometry. Maps between manifolds, pull-back, push forward. Diffeomorphisms. Derivatives without connection: exterior and Lie. Isometries, Killing Vectors.
Chapter 2: Maximally symmetric spaces
Generalities. Minkowski space as an excuse to learn about causal structure and Penrose diagrams. de Sitter space. Causality (out of order). Horizons. Anti de Sitter space.
Chapter 3: Elements of Cosmology
Homogeneous and Isotropic Spaces. FRW metric. Friedmann Equations. Distance measurements; Age of Universe.
Chapter 4: Black Holes I
Schwarzschild Metric. Birkhoff's Theorem. Singularities. Geodesics. Red Shift. Kruskal coordinates and extension. Penrose Diagrams.
Chapter 5: Black Holes II
More General Black Holes. Charged Holes. Spinning Holes. Penrose Process, Hawking Temperature.
Chapter 6: Other topics??
Tetrads, spinors, etc. Singularity theorems. Hawking radiation.
