Physics 5240, Spring 2015

Michael Fowler

We will pretty much follow the order of material as presented by Schutz.

1. A quick review of Special Relativity: the Lorentz transformations, paradoxes, etc. 

2. The formal apparatus of General Relativity in the special relativistic (flat space time) context: vectors, one-forms, tensors, the metric, etc.

3. Fluids in flat space time: flux, the stress-energy tensor, viscosity.

4. The Equivalence Principle, the need for curvilinear coordinates, and the generalization of vectors, one-forms, tensors to curved space, Christoffel symbols, geodesics, Riemann’s curvature tensor, Ricci and Einstein tensors, etc.

5. The Einstein Field Equations, we take the weak field limit to find Newton’s gravitational equation.

6. Gravitational Waves.

7. Spherically symmetric space times:  Schwartzschild metric, inside a star.

8. Black holes:  geodesics, Kruskal coordinates, Penrose diagrams, Kerr orbits, Hawking radiation.

9. Cosmology: the Cosmological Principle, Robertson-Walker metric, Friedmann equations, Hubble parameter, critical density, the Cosmological Constant, Redshift, flatness problem.