| Week beginning: | Material to be Discussed |
| 16 January |
Special Relativity: Review
[Carroll, Ch. 1 {Schutz, Chs. 1-3)] 4-vectors, Minkowski diagrams, an observer's future and past, simultaneity, light cones; {also signature} the Minkowski metric; Lorentz transformations, 4-momentum, 4-force and 4-acceleration; Maxwell's equations for E&M, and also fluids [Carroll, Ch. 1, {Schutz, Ch. 4}, handouts] |
| 23 January |
Manifolds, Tangent Vectors, (differential) 1-forms, Direct Products, Tensors as Multi-linear Operators on Vectors and 1-forms ; Tensor Transformation Laws; [Carroll, Ch. 2, {Schutz, Ch. 3}, handouts] non-holonomic Basis Vectors and (dual) Basis 1-forms [Carroll, App. J, {Schutz, 5.6}, handouts] |
| 30 January |
How do Tensors Change from one point to another? Tensor Bundles; Covariant Derivatives, [Carroll, Ch. 3 & App. B, {Schutz, Chs. 5-6}, handouts] |
| 6 February |
Affine Connections and their Curvatures; Examples; the Energy-Momentum Tensor, Tµ 
[Carroll, Chs. 3-4, {Schutz, Chs. 7-8}, handouts] |
| 13 February |
Affine Connections, Curvature and Geodesic Deviation Calculation Schemes for Connections and Curvatures; Einstein's Vacuum Field Equations: a Generalization of Newton's Grav. Eqns. and the full Grav'l Field Equations [Carroll, Chs. 3-4, {Schutz, Chs. 7-8}, handouts] |
| 20 February |
Spherical Symmetry; Lie Derivatives, Killing Vectors, and the Schwarzschild Solution(s) for stars. Meanings for Coordinate; [Carroll, Ch. 3.8 & 5, {Schutz, Ch. 10}, handouts] |
| 27 February | Catch-up for the Syllabus, Review, and Examination this week! |
| 6 March |
(test-particle) Orbits near a star,
and the standard "experimental tests"; Schwarzschild, Eddington, and Kruskal Coordinates: How do we interpret all this? Gravitational Binding Energy for stars; Collapse to a Black Hole; Conformal Diagrams [Carroll, Ch. 5 & App. G, {Schutz, Ch. 11}] |
| 13 March | Spring Break |
| 20 March | Uniformly accelerating Observers; Rotating, and/or Charged, Black Holes; Where is ``Elsewhere''? Latest Thoughts on the Quantum Layer above a Black Hole, and Black Hole Collisions. [Carroll, Ch. 6, {Schutz, Ch. 11}] |
| 27 March |
Probable Continuing to Look at Rotating Black Holes; Intro. to Gravitational waves: the linear approximation. How would a Passing Gravitational Wave be Perceived? [Carroll, Ch. 7, {Schutz, Ch. 7}] |
| 3 April |
Shear, Expansion, and Twist: properties bundles of null geodesics; ``Optical Properties'' of geodesic congruences, and Raychaudhuri's Theorem; Exact gravitational Waves; [Carroll, Ch. 7 & App. F, {Schutz, Ch. 9}, handouts] |
| 10 April |
Exact, twisting gravitational Waves; Petrov's Classification Theorem, and the use of symmetries to find solutions; Spinors in General Relativity; [Carroll, Ch. 7, {Schutz, Ch. 9}, handouts] |
| 17 April |
Maximally-Symmetric Spacetimes, and Bianchi Models; Friedmann-Robertson-Walker Universes, a Foundation for Cosmology [Carroll, Chs. 3.9 & 8, {Schutz, Ch. 12}, handouts] Term project outlines due! |
| 24 April |
Could we ever decide if the Universe is Open, Closed, or spatially
flat? Does the cosmological constant matter? |
| 1 May | More Thoughts on Cosmology or other open topics! |