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 as black holes,
gravitational waves astronomy, and cosmology.
You can find the course syllabus here
Monday and Wednesday 11:30am-12:45pm, in PAIS 1140.
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.
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.
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.
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 Reading |
Class Notes | Homework | HW Due | Solutions |
| Week 1 01/17-01/23 |
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 |
01/24 |
Homework #1 Solutions |
| Week 2 01/24-01/30 |
Four-vectors, index notation, and the metric | 01/24: Moore Ch. 2 01/29: Moore Ch. 3 - 4 |
Four-vectors Index notation and the metric |
Homework #2 |
01/31 |
Homework #2 Solutions |
| Week 3 01/31-02/06 |
More indices
and arbitrary coordinates |
01/31: Moore Ch. 4 02/05: Moore Ch. 5 |
Coordinate
bases |
Homework #3 |
02/07 |
Homework #3 Solutions |
| Week 4 02/07-02/13 |
Tensors |
02/07: Moore Ch. 5 - 6 02/12: Moore Ch. 6 |
Tensors |
Homework #4 |
02/14 |
Homework #4 Solutions |
| Week 5 02/14-02/20 |
Classical field theory and
geodesics |
02/14: Moore Ch. 7 02/19: Moore Ch. 8 |
U(1) Gauge
theory Geodesics Levi-Civita symbol |
Homework #5 |
02/21 |
Homework #5 Solutions |
| Week 6 02/21-02/27 |
Covariant derivative and Curvature | 02/21: Moore Ch. 17 02/26: Moore Ch. 18 |
Covariant
derivatives Curvature |
Homework #6 |
02/28 |
Homework #6 Solutions |
| Week 7 02/28-03/05 |
Riemann tensor, Ricci tensor and
Ricci scalar. |
02/28: Moore Ch. 19 03/04: Review |
Riemann
& Ricci tensors Review session |
Homework #7 |
03/05 |
Homework #7 Solutions |
| Week 8 03/06-03/08 |
Midterm Exam 03/06 |
Midterm Exam
Solutions |
||||
| Week
9 03/11-03/15 |
Spring
Break -No Class |
|||||
| Week 10 03/18-03/22 |
Energy-momentum tensor and the
Einstein Equation |
03/18: Ch. 20 03/20: Ch. 21 |
The
stress-energy tensor The Einstein Equation |
Homework #8 |
03/22 |
Homework #8 Solutions |
| Week 11 03/25-03/29 |
Einstein Equation and Schwarzschild Solution | 03/25: Ch. 22 03/27: Ch. 23 |
The
weak-field limit The Schwarzschild Solution |
Homework #9 |
03/29 |
Homework #9 Solutions |
| Week 12 04/01-04/05 |
Schwarzschild Solution and Black holes | 04/01: Ch. 9 04/03: Ch. 10 |
Properties
of Schwarzschild solution Particle orbits |
Homework #10 |
04/05 |
Homework #10 Solutions |
| Week
13 04/08-04/12 |
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 |
04/15 |
Homework #11 Solutions |
| Week 14 04/15-04/19 |
Gauge Freedom and Gravitational waves | 04/15: Ch. 30 04/17: Ch. 31 |
Gauge
Freedom Gravitational waves |
Homework
#12 |
04/19 |
Homework #12 Solutions |
| Week 15 04/22-04/26 |
Gravitational wave generation and energy | 04/22: Ch. 32 04/24: Ch. 33 |
Gravitational
wave energy Gravitational wave production |
Homework #13 |
04/26 |
Homework #13 Solutions |
| Week 16 04/29-05/03 |
Cosmology + Final Presentation |
04/29: Ch. 25-26 05/01 and 05/03: Presentations |
The FRLW
metric The Friedman equation |
Homework #14 |
05/03 |
Homework #14 Solutions |
| Date | Material, Problems or extra reading | Solutions |
| 01/17/2024 |
Extra Problem #1 |
Extra
Problem #1 Solutions |
| 01/25/2024 |
Extra Problems #2 |
Extra
Problems #2 Solutions |
| 02/01/2024 |
Extra Problems #3 |
Extra
Problems #3 Solutions |
| 02/08/2024 |
Extra Problems #4 |
Extra
Problems #4 Solutions |
| 02/14/2024 |
Extra Problems #5 |
Extra
Problems #5 Solutions |
| 02/19/2024 |
Extra Problems #6 |
Extra Problems
#6 Solutions |
| 02/26/2024 |
Extra Problems #7 |
Extra
Problems #7 Solutions |
| 03/04/2024 |
Extra Problems #8 |
Extra
Problems #8 Solutions |
| 03/18/2024 |
Extra Problems #9 |
Extra
Problems #9 Solutions |
| 03/25/2024 |
Extra Problems #10 |
Extra
Problems #10 Solutions |
| 04/01/2024 |
Extra Problems #11 |
Extra
Problems #11 Solutions |
| 04/15/2024 |
Extra Problems #12 |
Extra
Problems #12 Solutions |
| 04/22/2024 |
Extra Problems #13 |
Extra
Problems #13 Solutions |
| 04/29/2024 |
Extra Problems #14 |
Extra
Problems #14 Solutions |
