General Relativity -- PHYS-GA 2060

Fall 2018



Professor: Yacine Ali-Haïmoud
Lectures: Tuesdays and Thursdays 9:30AM - 10:45AM, Physics building (726 Broadway) room 902
Office Hours: Mondays 9:30 - 10:30AM, Physics building office 939.

Homeworks will be posted on Tuesdays, due the following Tuesday in class. Handwritten homeworks are acceptable provided they are clearly and cleanly written.
The final will consist of a project, with a written report and an oral presentation to class on December 11 and 13 (mark your calendars!)

Grading: bare grade = 50% homework + 20% midterm + 30% final exam.
Attendance below 50% is penalized, attendance above 50% is rewarded:
renormalized grade = (bare grade)1/(attendance + 0.5)
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%.

Course description: Manifolds, vectors and tensor fields, curvature and gravitation; applications to black holes, relativistic stars, cosmology and gravitational waves.

Recommended textbook: Sean Carroll's Spacetime and Geometry: An Introduction to General Relativity.
Sean Carroll's lecture notes (an abridged, preliminary version of his book) are available here.

Other great textbooks:
Robert Wald's General Relativity
Steven Weinberg's Gravitation and Cosmology
Misner, Thorne and Wheeler's Gravitation (MTW)
Thorne and Blandford's Modern Classical Physics (chapters 1-2, 24-28).


Lectures

--- Part I: Mathematical foundations and formulation of GR ---

Week 1 (9/04, 9/06): review of special relativity, vectors and tensors. Lectures 1 and 2
Week 2 (9/11, 9/13): ideal fluid, electromagnetism, equivalence principle (lecture 3), manifolds (lecture 4)
Week 3 (9/18, 9/20): metric tensor field (lecture 5), covariant derivatives (lecture 6).
Week 4 (9/25, 9/27): from special to general relativity, the Riemann curvature tensor (lecture 7 and lecture 8).
Week 5 (10/2, 10/4): Einstein field equation (lecture 9), integration and Einstein-Hilbert action (lecture 10)

--- Part II: Linearized gravity; gravitational waves ---

Week 6 (10/9, 10/11): Linearized gravity (lecture 11), linearized Einstein field equations (lecture 12).
Week 7 (10/16, 10/18): Far-field metric of a quasi-Newtonian source (lecture 13), Lense-Thirring effect, gravitational redshift and deflection of light (lecture 14).
Week 8 (10/23, 10/25): Gravitational lensing and Shapiro time delay (lecture 15). Gravitational waves: polarization and generation by a circular binary (lecture 16).
Week 9 (10/30, 11/01): Energy-momentum of gravitational waves; orbital decay of a circular binary. Introduction to the post-Newtonian expansion (lecture 17 and lecture 18).

--- Part III: Symmetric spacetimes: relativistic stars and black holes; cosmology ---

Week 10 (11/06, 11/08): Symmetries, Spherically-symmetric spacetimes (lecture 19. The Schwarzschild solution (lecture 20).
Week 11 (11/13, 11/15): Midterm exam (solution). Spherically-symmetric stationary stars (lecture 21).
Week 12 (11/20, 11/22): Timelike geodesics of Schwarzschild (lecture 22). Thanksgiving.
Week 13 (11/27, 11/29): Schwarzschild black holes (lecture 23), Penrose diagrams and Kerr black holes (lecture 24).
Week 14 (12/04, 12/06): Introduction to cosmology (lecture 25), review of the semester.

Week 15 (12/11, 12/13): Final oral presentations starting at 9:10 am.

Homeworks

Hand-written homeworks are acceptable only if they are clearly legible.

homework 1 (due Sept 11). solution
homework 2 (due Sept 18). solution
homework 3 (due Sept 27). solution
homework 4 (due Oct 4). solution
homework 5 (due Oct 11). solution
homework 6 (due Oct 18). solution
homework 7 (due Oct 25). solution
homework 8 (due Nov 1st). solution
homework 9 (due Nov 8th). solution



Last updated December 6th, 2018