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.

renormalized grade = (bare grade)

Examples: If you have a perfect bare grade, attendance will not affect it.

If you have a bare grade of 50% but have attended all lectures, your renormalized grade will be 63%.

If you have a bare grade of 50% but only attended 1/10 of the lectures, your renormalized grade will be 31%.

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 3): warm up with spatial distances, notion of spatial metric, coordinate transformations.

lecture 2 (Sept 5): introduction to inertial coordinate systems and spacetime intervals.

lecture 3 (Sept 10): inverse metric, measurements in a particle's rest frame, geodesic equation.

lecture 4 (Sept 12): the equivalence principle, gravitational redshift, preliminaries on curvature.

lecture 5 (Sept 17): manifolds and tangent vectors.

lecture 6 (Sept 19): dual vectors and tensors.

lecture 7 (Sept 24): basic operations on tensors, tensor fields.

lecture 8 (Sept 26): covariant derivatives.

lecture 9 (Sept 30): parallel transport, geodesics again, generally covariant equations.

lecture 10 (Oct 1): charge conservation, electromagnetism, stress-energy tensor.

lecture 11 (Oct 8): the Riemann tensor: definition and basic properties.

lecture 12 (Oct 10): Riemann as a measure of curvature; Fermi normal coordinates.

lecture 13 (Oct 11): geodesic deviation; Einstein field equations, Lagrangian formulation.

lecture 14 (Oct 15): warm-up with electromagnetism; gauge transformations and scalar-vector-tensor decomposition.

lecture 15 (Oct 17): linearized Einstein field equations.

lecture 16 (Oct 25): far-field metric of a quasi-Newtonian source.

lecture 17 (Oct 29): gravitational redshift, deflection of light and Shapiro time delay.

lecture 18 (Nov 1): power radiated by gravitational waves; merger of a circular binary.

lecture 19 (Nov 5): symmetries; spherically symmetric spacetimes; Schwarzschild solution.

lecture 20 (Nov 7): timelike geodesics of Schwarzschild.

lecture 21 (Nov 12): spherically symmetric and stationary stars.

lecture 22 (Nov 14): Schwarzschild black holes: extended Kruskal coordinates, Penrose diagrams.

lecture 23 (Nov 21): polarizations of gravitational waves and generation by a circular binary.

lecture 24 (Nov 25): Kerr (i.e. spinning) black holes.

lecture 25 (Dec 3): introduction to gravitational lensing and the post-Newtonian expansion.

lecture 26 (Dec 5): introduction to cosmology (guest lecture by Masha Baryakhtar)

lecture 27 (Dec 10): introduction to numerical relativity (guest lecture by Masha Okounkova)

lecture 28 (Dec 12): student presentations

Posted on Tuesdays, due the following Tuesday in class.

Hand-written homeworks are acceptable only if they are

homework 1 (due Sept 10). solution.

homework 2 (due Sept 17). solution.

homework 3 (due Sept 24). solution.

homework 4 (due Oct 1). solution.

homework 5 (due Oct 8). solution.

homework 6 (due Oct 15). solution.

homework 7 (due Oct 25). solution.

homework 8 (due Nov 5). solution.

homework 9 (due Nov 12). solution.

The

The

• You may pick a topic of your choice, and could for instance explore one of the topics covered in class in greater depth.

You must

Below is a non-exhaustive list of possible topics. For more ideas, and for references, a great resource is Living reviews in Relativity .

-Post-Newtonian perturbation theory and evolution of a binary system.

-Black hole perturbations.

-The gravitational self-force and point-particles in relativity.

-Laser-interferometer gravitational-wave detectors.

-Pulsar timing arrays.

-Relativistic accretion disks.

-Neutron stars.

-Experimental tests of general relativity.

-Non-Schwarzschild black holes.

-Modified theories of gravity.

-Cosmological perturbation theory.

-Explain the EHT observations.

• The written report must be typed up

It must include an exhaustive list of references. Here is an example latex source code.

Please

• The oral presentation on Thursday 12/12 will be

You will not have time to derive everything that is in your project, but are expected to highlight the major steps and important results.