Professor: Yacine Ali-Haïmoud

Lectures: Tuesdays and Thursdays 9:30AM - 10:45AM, Physics building (726 Broadway)

Office Hours: Mondays 9:30 - 10:30AM, Physics building office 939.

Grading: 30% homework, 30% midterm, 30% final exam, best of 3 gets 10% extra weight.

Sean Carroll's lecture notes (an abridged, preliminary version of his book) are available here.

Other great textbooks:

Robert Wald's

Steven Weinberg's

Misner, Thorne and Wheeler's

Thorne and Blandford's

lecture 1 (Sept 05): Linear algebra, vectors and tensors.

lecture 2 (Sept 07): Introduction to the tangent space, coordinate bases.

lecture 3 (Sept 12): Special relativity.

lecture 4 (Sept 14): Kinetic theory. The equivalence principle.

lecture 5 (Sept 19): Manifolds.

lecture 6 (Sept 21): Covariant derivatives.

lecture 7 (Sept 26): Curvature.

lecture 8 (Sept 28): The Riemann tensor.

lecture 9 (Oct 03): Einstein's field equation.

lecture 10 (Oct 05): Killing vectors, conservation laws, Lagrangian formulation of GR.

lecture 11 (Oct 10): Gauge transformations, scalar-vector-tensor decomposition.

lecture 12 (Oct 12): Linearized Einstein field equations.

lecture 13 (Oct 17): Far-field metric of a quasi-Newtonian source.

lecture 14 (Oct 19): Lense-Thirring effect, gravitational redshift, deflection of light.

-- no lecture on Oct 24 (midterm exam).

lecture 15 (Oct 26): Gravitational lensing, Shapiro time delay, effect of gravitational waves.

lecture 16 (Oct 31): Generation of gravitational waves, application to a circular binary.

lecture 17 (Nov 02): Energy of gravitational waves. Quadrupole formula for the power radiated in GWs.

lecture 18 (Nov 07): Angular momentum radiated in gravitational waves. Introduction to the post-Newtonian expansion.

lecture 19 (Nov 09): Symmetries. Spherically symmetric spacetimes.

lecture 20 (Nov 14): Birkhoff's theorem, the Schwarzschild metric, orbits of massive particles.

lecture 21 (Nov 16): Introduction to pulsar timing arrays (guest lecture by Dr. Chiara Mingarelli).

lecture 22 (Nov 21): Periastron precession. Tollmann-Oppenheimer-Volkov equations of stellar structure.

lecture 23 (Nov 28): Constant-density star. Embedding diagrams. Kruskal extension for Schwarzschild black holes.

lecture 24 (Nov 30): Conformal transformations and diagrams.

lecture 25 (Dec 05): Kerr metric. FLRW metric.

lecture 26 (Dec 07): Brief introduction to cosmology basics.

Homeworks will be posted on Tuesday and due the following Tuesday.

You can type them up or hand-write them, I only require that they are

homework 1 (due Sept 12). solution

homework 2 (due Sept 19). solution

homework 3 (due Sept 26). solution

homework 4 (due Oct 03). solution

homework 5 (due Oct 10). solution

homework 6 (due Oct 17). solution

-- no homework due Oct 24 (midterm exam)

homework 7 (due Oct 31). solution

homework 8 (due Nov 07). solution

homework 9 (due Nov 14). solution and mathematica notebook

Midterm (to be presented orally on Oct 24). solution

Instructions for the final project.