Relativity Theory I (2017-18) -- PHY483F/1483F
This course will introduce General Relativity from a physics point of view, emphasizing a modern perspective. I will begin with a review and rephrasing of special relativity, including the case of constant acceleration. Then I will motivate curved spacetime, the covariant derivative, and the Christoffel connection. I will derive the equation for a geodesic, the analogue of a straight line in curved spacetime. From there, I will develop the Riemann curvature tensor, and show how it encodes useful physics like tidal forces and geodesic deviation. Then I will introduce the famous Einstein equations and show how they can be used to study equations for stars and black holes. I will showcase some of the experimental successes of GR, before finishing up with a description of the origin of Einstein's equations starting from an action principle and a brief introduction to cosmology. (For more details, please see the syllabus.)
Classes are held on Mondays and Thursdays from 11:10-12:00 and tutorials are held on Fridays from 13:10-14:00, both in MP134. My regular weekly office hours are held on Tuesdays from 16:15-18:00 in MP1118.
Tips for understanding lectures
I frequently update the lecture notes to make them clearer and to remove typos, after questions that I get (a) in class, (b) after class in the corridor, and (c) during office hours. So if some point in the lecture notes didn't seem clear the first time you tried reading about a concept, try reloading the notes to see if there is an upgraded explanation. You can tell if I have updated the notes because I put a fresh date stamp for each new version on the front page.
It is often easier to get confident with the material if you read the lecture notes before class. I never cover more than about 6 pages per lecture, so if you read the next 6 pages beyond where we finished last time, you should find classes easier. I welcome questions in class, as long as asking them is likely to benefit other students as well as you. If your question is more individual, I am happy to answer it to your heart's content in office hours.
These will be posted in reverse chronological order, to make the latest ones easiest to find.
- F08Dec: a student asked after class if there is a good source to learn about concepts like the multiverse. There is a big literature about this; I think Max Tegmark's site is a pretty good starting point.
- R07Dec: I would like to offer a very big thank you to everyone enrolled in or auditing the course -- you are a great bunch of students and it has been a genuine pleasure teaching you this semester. I wish each of you good luck for the final exam on Saturday, and for your future adventures, whatever they may involve. Please also be confident in the knowledge that my respect for you is not dependent on your grade performance (that is one of my teaching principles). If you have any last-minute questions for me before the exam, I will be answering emails/phone calls/voicemails as quickly as possible. Any students interested in asking followup questions after exams are over (e.g. next semester) is welcome to do so. Please note that uncollected homework assignments are in my office and you will need to collect them from me directly. Please also note that I have done a final update of the lecture notes this afternoon; the final page count is 133 pages plus 22 pages of appendix.
- W29Nov: thanks to three very alert students who visited my office hours and corresponded with my by email, I found typos in eq.(5) and eq.(11) of problem 4.4 of HW4, which stemmed from a sign error in the definition of Riemann. I have gone back and corrected all the relevant formulae in the lecture notes as well as the HW4 typos. Please reload both, and sorry for the bother!
- M27Nov: my last major update of parts of the lecture notes is complete.
- W22Nov: here are some general tips about what will be on the final exam, along with six sample problems for you to practice solving.
- W22Nov: the remaining office hours for me and the TA are as follows.
Students may also make individual appointments to see me at other times. To book a private appointment, follow the instructions given on my contact page.
- Me: Tue.28.Nov and Tue.05.Dec at 16:15-18:00.
- TA: Mon.27.Nov and Mon.04.Dec from 16:30-17:30.
- W22Nov: lecture notes have been updated. In particular, a confusing typo in eq.(6.65) on p.69 near the end of section 6.3 on Geodesics of Schwarzschild has been corrected. Thanks to a very conscientious student for pointing it out to me in office hours.
- R16Nov: Homework 4 is posted. It is qualitatively a bit different in style than HW1-3, so I will be providing copious hints in office hours on T21Nov and T28Nov, which will be held in the MP408 classroom on the 4th floor of the Burton Tower in MP building.
- F10Nov, updated S12Nov: I have significantly updated the lecture notes, adding a chapter on gravitational waves which I will cover in the week of Nov.20, after I discuss experimental successes of GR in the week of Nov.13. The cosmology section for the week of Nov.27 is not finished yet. Further updates will be completed soon.
- M06Nov and T07Nov: Yes, I will be holding office hours at the usual time this week, even though it is Reading Week.
Also, please note that I have corrected a small typo in eq.(5) of Q3 in Homework 3, and made clearer how I want you do part (d) of Q3. Please re-download the assignment to see both these new corrections.
- R02Nov: good luck on the midterm this evening! Homework 3 is posted.
- R26Oct: Today's lecture is the cutoff for what might be on the midterm. I will not be examining any material discussed next week until the final exam.
- W25Oct: As promised, here are some pertinent old midterm questions to try.
- R12Oct: I have significantly updated the lecture notes compared to this morning, to make them more comprehensible and less full of extraneous technical detail. I hope the clarifications (and typo corrections) make studying the ideas easier for all of you.
- W11Oct: After input from students in my office hours yesterday, I have updated HW2 to correct a sign typo and make clearer how I want you to solve all three problems. Please re-download the HW2 PDF to ensure that you get these updates.
- R05Oct: Please ensure that you get any late homework assignments directly to the TA. The best place to hand them in tomorrow within the grace period is at the tutorial. Please also ensure that your assignment is firmly stapled together with a proper metal staple (either that or write your name and student number and the page number on every page of your assignment). Why do I insist on proper stapling? Well, sometimes a professor or a TA accidentally drops a handful of assignments on the floor, and we would not want your work to get mixed up with that of another student. If you want to hand in your assignment after the grace period, and I or the TA are not in our offices, you can hand in during business hours to the Physics Undergraduate Coordinator on the 3rd floor of Burton Tower in MP301.
- R05Oct: Homework 2 is posted. All of the concepts needed for these problems have been covered in lectures so far. Please note: if you find the problems too difficult or too long, please let me know. I am always willing to adjust my teaching in response to student concerns, especially when it comes to workload. I do not want my GR course to be your worst-ever experience in terms of homeworks!
- W27Sep: I have corrected a typo in eq.(2) in HW1 which resulted in a wayward minus sign. Thanks to an alert student for pointing this out. Please reload the PDF.
- T26Sep: Currently I am really jammed up on typing, because of a national CAP responsibility (including a two-day trip to Ottawa on Friday), and because it is recommendation letter season for postdoc and faculty jobs. Typing is routinely painful for me because of chronic pain caused by a major skiing accident years ago. Please try to respect my disability constraints by seeking my physics assistance verbally rather than textually, where feasible. (If you only feel comfortable interacting with me textually, we can arrange a Skype where I speak to make input and you type to make input.) I do not have many available meeting spots remaining this week, but I can still book Skype/FaceTime meetings with any student needing my assistance even if we cannot meet in person. Email me for an appointment by stating all times you are available -- I will reply with confirmation of an appointment time.
- T26Sep: Plain-language lecture summaries have been moved here. I will continue typing them up, on top of improving my lecture notes, only if my pain burden permits it. Thank you in advance for your understanding if I am sometimes not able to manage this. I prioritize (a) helping students in person and (b) typing upgrades to the lecture notes in response to student questions in class, in the corridor, and in office hours.
- R21Sep: Homework 1 is posted. You already have the tools to do Q1 and Q2; by this time next week we will have covered everything you need for Q3 as well. Start on Q1 and Q2 now, and feel free to make full use of my office hours (Tuesdays 16:15-18:00 in MP1118) to ask any question you like about HW1. Please let me know if you find any typos in the questions: I like to fix them ASAP.
- W20Sep: This is a note for all students, but especially new graduate students who may not yet be familiar with all UofT procedures. Remember: the primary mechanism UofT uses to send you course-related email announcements is your UTmail+ (@utoronto.ca) account, *not* your departmental account. Make sure you have your email app configured to send and receive UTmail+ as well as departmental email. Also, note that you need to learn how to use Blackboard, our UofT courseware, in order to access online tutorial notes from the TA. Log in to portal.utoronto.ca to get started.
- F08Sep: The TA has brought to my attention the fact that the room for our tutorial has been changed to MP134. I really apologize for the confusion!
- R03Aug: The first day of class will be Thursday 7th September at 11am in MP134, and I look forward to meeting you all. Bring your calendars: we will decide on my office hours together.