PHYS 480/581: General Relativity

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

Teaching assistant
Mr. Keith Sanders
Office: Zoom, Thursdays 2-4pm

Our Slack channel can be found here. Email me if you need an invitation.

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!

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 as gravitational waves astronomy, cosmology, black holes, and solar system tests of GR.

Final Presentations on Zoom this week. Final exam scheduled for Monday 12/07 9am.

The schedule for the final presentations is here.

Syllabus: Please read carefully!!

You can find the course syllabus here

Meeting times

Monday and Wednesday 4:00-5:15pm, in PAIS 1140 or on Zoom. The meeting password and direct link to connect should have been emailed to you. Note that you will need to log in to Zoom with your UNM NetID to access the call.

Even if some of us meet in person, there will always be the option of joining the class via Zoom. Whether or not we meet in person on a given day will be posted in the schedule below. The Zoom meetings will be recorded and posted on the UNM Learn course page.

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 (either in person or through Zoom). 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! With the current pandemic and related social distancing rules, having casual conversations around science and physics is nearly impossible. 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. One of the hour will be reserved to discuss more advanced topics that will (hopefully!) help you better understand what ``under the hood'' of GR. This last hour will be mostly aimed at graduate students, but of course, everyone is welcome to join.

Grab a cup of coffee (or tea!), and join me for some casual conversation about physics!
Tuesdays 3:00-4:00pm and Thursdays 1:00-2:00pm on Zoom.

Final Projects

You can find here the list of potential topics for your Final Project. You are encouraged to pursue other topics that interest you. Consult with me in advance. Once you've chosen a topic, please let me (and everyone else) know by posting your choice in the #final-projects channel on Slack. 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 login information necessary to access the homework PDFs will be provided in the first class. The homework must be submitted on the UNM Learn platform at 5pm on the day they are 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 Where Subject   Pre-class
Class Notes Homework HW Due Solutions
Week 1
08/17: Zoom
08/19: Zoom
Equivalence Principle and Review of Special Relativity

08/19: Moore Ch. 2
Equivalence Princ.
Special Relativity Review
Homework 1
Homework 1 Solutions
Week 2
08/24: Zoom
08/26: Zoom
Lorentz transformations and four-vectors 08/24: Moore Ch. 2
08/26: Moore Ch. 3
Homework 2
Homework 2 Solutions
Week 3
08/31: Zoom
09/02: Zoom
Index Notation, Metric, and Arbitrary Coordinates
08/31: Moore Ch. 4
09/02: Moore Ch. 5
Index Notations
Coordinate Bases
Homework 3

Homework 3 Solutions
Week 4

09/09: Zoom
No Class on 09/07 (Labor Day)

09/09: Moore Ch. 6
Homework 4

Homework 4

Week 5
09/14: Zoom
09/16: Zoom
Classical Field Theory and more Tensors
09/14: Moore Ch. 7
Tensor test problem
Levi-Civita Example
Homework 5

Homework 5 Solutions
Week 6
09/21: Zoom
09/23: Zoom
Geodesics and Covariant Derivatives
09/21: Moore Ch. 8
09/23: Moore Ch. 17
Geodesic Equation
Covariant Derivatives
Homework 6

Homework 6 Solutions
Week 7
09/28: Zoom
09/30: Zoom
Curvature and Geodesic Deviation
09/28: Moore Ch. 18
09/30: Moore Ch. 19
Curvature Tensor
Riemann and Ricci
Homework 7

Homework 7 Solutions
Week 8

Midterm Exam 10/05
No Class on 10/07

No homework this week
 No homework this week
Midterm Solutions
Week 9
10/12: Zoom
10/14: Zoom
Energy-momentum Tensor and the Einstein Equation
10/12: Moore Ch. 20
10/14: Moore Ch. 21
Stress-energy tensor
Einstein Equation
Homework 8

Homework 8 Solutions
Week 10
10/19: Zoom
10/21: Zoom
Einstein Equation and Schwarzschild Solution
10/19: Moore Ch. 22
10/21: Moore Ch. 23
Einstein Equation Properties
Schwarzschild Solution
Homework 9

Homework 9 Solutions
Week 11
10/26: Zoom
10/28: Zoom
Schwarzschild Solution and Black holes 10/26: Moore Ch. 9
10/28: Moore Ch. 10
Schwarzschild Properties
Particle Orbits
Homework 10

Homework 10 Solutions
Week 12
11/02: Zoom
11/04: Zoom
Black Hole event horizon and Hawking Radiation
11/02: Moore Ch. 14
11/04: Moore Ch. 16
Event Horizon and Black holes
Hawking Radiation
Homework 11

Homework 11 Solutions
Week 13
11/09: Zoom
11/11: Zoom
Gauge Freedom and Gravitational waves
11/09: Moore Ch. 30
11/11: Moore Ch. 31
Gauge Freedom
Gravitational waves
Homework 12

Homework 12 Solutions
Week 14

11/16: Zoom
11/18: Zoom
Gravitational wave generation and energy
11/16: Moore Ch. 32
11/18: Moore Ch. 33
GW Energy
GW Production
Homework 13

Homework 13 Solutions
Week 15

11/23: Zoom
11/25: Zoom
Cosmology and the Hubble Expansion
11/23: Moore Ch. 24-25
11/25: Moore Ch. 26
Metric of the cosmos
The Friedmann Eqs.
Homework 14
Homework 14 Solutions
Week 16

Oral Presentations
Final Project due

Final Exam solutions

GR Coffee Hours Extra Material

Date Material, Problems or extra reading

You have the ability to prevent the spread of COVID-19 and to preserve the health of fellow students, your instructor, staff and the community by following UNM health protocols. The UNM Provost Administrative Directive on Mandatory Student Face Covering and Symptom Reporting of July 9, 2020 requires that all students on UNM-Main and UNM branch campuses wear face masks in the face-to-face classroom and on campus unless they have a specific mask accommodation (confidentially documented with the Accessibility Resource Center). UNM Provost Administrative Directive is consistent with Governor Lujan Grisham’s Public Health Emergency Order, as amended, and the Public Health Order of the New Mexico Health Secretary. It also requires daily participation in symptom screening through covidscreen, which will be sent via UNM e-mail.

Acceptable masks and mask wearing in class: A two-layer mask that covers the nose and mouth and that is cleaned regularly is acceptable. A face shield is not sufficient protection. It is vital that you wear your mask correctly, covering your nose and mouth. Removing your mask for an extended period to eat or drink in class violates the Provost Administrative Directive and endangers others.

Mask Wearing Accommodation: Individuals with a documented disability or diagnosis may seek accommodation with the UNM Accessibility Resource Center (ARC). Individuals do not need to reveal private information to an instructor. ARC will require documentation of health requirements, which will be kept confidential. The instructor will be informed only of any need for accommodation.

Consequences of not wearing a mask properly: Unless you have an ARC-approved accommodation, if you don’t wear a mask, or if you do not wear a mask properly by covering your nose and mouth, you will be asked to leave class. If you fail to wear a mask properly on more than one occasions, you can expect to be dropped from the class. If you insist on remaining in the classroom while not wearing a mask (without an ARC-determined accommodation), class will be dismissed for the day to protect others and you will be dropped from the class immediately.

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In accordance with University Policy 2310 and the Americans with Disabilities Act (ADA), academic accommodations may be made for any student who notifies the instructor of the need for an accommodation. It is imperative that you take the initiative to bring such needs to the instructor’s attention, as I am not legally permitted to inquire. Students who may require assistance in emergency evacuations should contact the instructor as to the most appropriate procedures to follow. Contact Accessibility Resource Center at (505) 277-3506 for additional information.

If you need an accommodation based on how course requirement interact with the impact of a disability, you should contact me to arrange an appointment as soon as possible. At the appointment we can discuss the course format and requirements, anticipate the need for adjustments and explore potential accommodations. I rely on the Accessibility Resource Center (ARC) Office for assistance in developing strategies and verifying accommodation needs. If you have not previously contacted them I encourage you to do so.

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