PHYS 480/581: General Relativity

Prof. Francis-Yan Cyr-Racine
Office: PAIS 3214

Teaching assistant
Mr. Kylar Greene
Office: Zoom, Fridays 1:30-2:30pm

Description of the class

General Relativity (GR) is one of the most beautiful theory ever invented! At its core, it links a phenomenon that we all experience -- gravity -- to the nature of spacetime itself and the energy and matter it contains. Using an elegant mathematical framework, GR details both how the very fabric of spacetime reacts to the presence of large matter concentrations, and how the latter evolve within this curved spacetime. GR has been extremely successful at describing observations from a range of length scales spanning over 30 orders of magnitude from the size of the observable universe to tabletop-sized experiments here on Earth. Recently, the first direct detection of gravitational waves has allowed us to directly probe GR near the event horizon of a black hole. Join me on this epic journey ton unveil the nature of spacetime itself!

This class is aimed at senior undergraduates and graduate students. In the first part of the course, we will establish the physical and mathematical language necessary to have grownup conversations about GR. This includes discussing four-vectors and index notations, reviewing Special Relativity and Lorentz transformation, introducing the metric and its related tensors, and discussing general coordinate systems. With this foundation established, the second part of the course will focus on the structure of curved spacetime and how to describe it with the tools and concepts introduced in the first part of the course. This will culminate with the derivation and interpretation of the Einstein equation, probably the most insightful equation ever derived. The third part of the course will cover applications of GR such a
s black holes, gravitational waves astronomy, and cosmology.

Final Exam to take place Monday May 6th 11am-1pm in room 1140.

Syllabus: Please read carefully!!

You can find the course syllabus here

Meeting times

Monday and Wednesday 11:30am-12:45pm, in PAIS 1140.

Class format

There will required readings (4-5 pages) before each class. These can be found in the schedule below. In addition, on a rotating basis, students will be asked to fill in the ``boxes'' in Moore's workbook, and present their solutions to the class. There will be a 5% "participation" grade associated with having your solution (when you are assigned a box) ready to present at class time. The rotating assignments for Moore's boxes will posted here.


Required textbook for the class
A General Relativity Workbook by Thomas A. Moore.

Additional resources
Spacetime and Geometry: An Introduction to General Relativity by Sean M. Carroll.
Gravity: an Introduction to Einstein's General Relativity by James B. Hartle.

GR Coffee hours!

We learn a lot by casually talking about physics with our peers. Much of the physics that I know I've learned that way! The GR coffee hours is my attempt to create a space where we (mostly you) can have casual conversations about GR and physics in general without the constraints of being in an actual class. Of course, you can show up to ask questions about the homework or the reading if you want. These will serve as my "office hours". Otherwise, we will go through key GR-related problems or discuss more advanced topics that will (hopefully!) help you better understand what is ``under the hood'' of GR. If you have a spare credit hour, you can register for my PHYS 551 (graduate students) or PHYS 451 (undergraduate students) course using  the CR/NC option. You will get the credit if you show up for at least 10 sessions.

Grab a cup of coffee (or tea!), and join me for some interesting conversation about GR!
Mondays and Thursdays 3:00-4:00pm in PAIS 2210.

Final Projects

The list of potential topics for your Final Project list is posted here. You are encouraged to pursue other topics that interest you. Consult with me in advance. Once you've chosen a topic, please let me know by email. I won't allow more than 2 students to choose the same topic. First come, first serve.

Homework assignments

There will be nearly weekly assignments during the semester. The assignments will be posted in the schedule about 7 days before they are due. The homework must be submitted on the UNM Canvas at 5pm on the day it is due. Late homework policy: homework returned in the next 24 hours after the due date will be accepted but with 30% penalization. After these 24 hours the corresponding solutions will be posted here, and your assignment won't be graded.

While I strongly encourage you to discuss the homework assignments with your classmates, the work you hand in must be entirely yours.


Date Subject   Pre-class
Class Notes Homework HW Due Solutions
Week 1
Equivalence Principle and Review of Special Relativity
01/17: Moore Ch. 1
01/22: Moore Ch. 2
The Equivalence Principle
Special Relativity Review
Homework #1
Homework #1 Solutions
Week 2
Four-vectors, index notation, and the metric 01/24: Moore Ch. 2
01/29: Moore Ch. 3 - 4
Index notation and the metric
Homework #2
Homework #2 Solutions
Week 3
More indices and arbitrary coordinates
01/31: Moore Ch. 4
02/05: Moore Ch. 5
Coordinate bases
Homework #3
Homework #3 Solutions
Week 4
02/07: Moore Ch. 5 - 6
02/12: Moore Ch. 6
Homework #4
Homework #4 Solutions
Week 5
Classical field theory and geodesics
02/14: Moore Ch. 7
02/19: Moore Ch. 8
U(1) Gauge theory
Levi-Civita symbol
Homework #5
Homework #5 Solutions
Week 6
Covariant derivative and Curvature 02/21: Moore Ch. 17
02/26: Moore Ch. 18
Covariant derivatives
Homework #6
Homework #6 Solutions
Week 7
Riemann tensor, Ricci tensor and Ricci scalar.
02/28: Moore Ch. 19
03/04: Review
Riemann & Ricci tensors
Review session
Homework #7

Homework #7 Solutions
Week 8

Midterm Exam 03/06

Midterm Exam Solutions
Week 9
Spring Break -No Class

Week 10
Energy-momentum tensor and the Einstein Equation
03/18: Ch. 20
03/20: Ch. 21
The stress-energy tensor
The Einstein Equation
Homework #8
Homework #8 Solutions
Week 11
Einstein Equation and Schwarzschild Solution 03/25: Ch. 22
03/27: Ch. 23
The weak-field limit
The Schwarzschild Solution
Homework #9
Homework #9 Solutions
Week 12
Schwarzschild Solution and Black holes 04/01: Ch. 9
04/03: Ch. 10
Properties of Schwarzschild solution
Particle orbits
Homework #10
Homework #10

Week 13
Black Hole event horizon and Hawking Radiation 04/08: Total Eclipse (No class!)
04/10: Ch. 14
04/12: Ch. 16 (Special class)
Event horizon and Einstein-Rosen bridges
Hawking Radiation
Homework #11
Homework #11 Solutions
Week 14

Gauge Freedom and Gravitational waves 04/15: Ch. 30
04/17: Ch. 31
Gauge Freedom
Gravitational waves
Homework #12
Homework #12 Solutions
Week 15

Gravitational wave generation and energy 04/22: Ch. 32
04/24: Ch. 33
Gravitational wave energy
Gravitational wave production
Homework #13
Homework #13 Solutions
Week 16
Cosmology + Final Presentation
04/29: Ch. 25-26
05/01 and 05/03: Presentations
The FRLW metric
The Friedman equation
Homework #14
Homework #14 Solutions

GR Coffee Hours Extra Material

Date Material, Problems or extra reading Solutions
Extra Problem #1
Extra Problem #1 Solutions
Extra Problems #2
Extra Problems #2 Solutions
Extra Problems #3
Extra Problems #3 Solutions
Extra Problems #4
Extra Problems #4 Solutions
Extra Problems #5
Extra Problems #5 Solutions
Extra Problems #6
Extra Problems #6 Solutions
Extra Problems #7
Extra Problems #7 Solutions
Extra Problems #8
Extra Problems #8 Solutions
Extra Problems #9
Extra Problems #9 Solutions
Extra Problems #10
Extra Problems #10 Solutions
Extra Problems #11
Extra Problems #11 Solutions
Extra Problems #12
Extra Problems #12 Solutions
Extra Problems #13
Extra Problems #13 Solutions
Extra Problems #14
Extra Problems #14 Solutions