General Relativity

Lecturer: Ian McArthur

1. Review of special relativity.
2. Metrics, the spacetime interval and curved spacetimes.
3. Local coordinate systems and the transformation between coordinate systems, tensors.
4. The principle of equivalence and locally inertial coordinate systems.
5. Gravitational time dilation and redshift.
6. Geodesics, Christoffel symbols, reduction of geodesic equation to Newtonian limit in weak fields.
7. Solving the geodesic equation for the Schwartzschild metric, precession of planetary perihelia, bending of light in gravitational field, comparison with experiment.
8. Parallel transport and its relation to curvature.
9. The curvature tensor and its physical significance.
10. Einstein's equations.
11. Gravitational waves
12. Black holes