Description of the Class
General Relativity (GR) is one of the most beautiful theories 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 to 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 gravitational-wave astronomy, black holes, classical tests, frame-dragging, and exotic spacetimes.
Class Format
There will be 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. Part of the final grade will be 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 be posted here. There will also be in-class worksheets for which students will be asked to work in small groups. Part of the final grade will include completing these worksheets. If you are absent when a worksheet is assigned, you will have one week to complete it and hand it in to me for grading.
Grading Scheme
- 25% Presenting solutions to Moore's boxes/In-class worksheets
- 20% Homework assignments
- 25% Midterm exam
- 30% Final exam
GR Problem Hour
The GR problem hour is my attempt to create a space where we can solve GR problems outside of the actual class. Of course, you can show up to ask questions about the homework or the reading if you want. This problem hour will supplement my office hours. 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.
Join me for some interesting problems about GR! Thursdays, 3–4pm, in PAIS 1140.
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 UNM Canvas at 8pm 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 a 25% penalty (meaning that the maximum grade you can get on that assignment is 75%); assignments submitted up to 48 hours after the deadline will be accepted with a 50% penalty. After these 48 hours, the corresponding solutions will be posted in the schedule, 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. See also the AI-use policy in the syllabus.