At students' request I will be scanning 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!
- Review of elements of differential geometry
- Maps between manifolds, pull-back, push forward
- Diffeomorphisms
- Derivatives without connection: exterior and Lie
- Isometries, Killing Vectors
- 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
- Elements of Cosmology
- Homogeneous and Isotropic Spaces
- FRW metric
- Friedmann Equations
- Distance measurements; Age of Universe
- Black Holes
- Schwartzschild
- More General Black Holes, Charged Holes
- Spinning Holes, Pensrose Process, Hawking Temperature
- Other topics??
- Tetrads, spinors, ...
- Singularity theorems
- Hawking radiation