PHY483F

Relativity Theory I (2020-21) -- PHY483F/1483F

Syllabus

Topics

Special relativity and tensors: Galilean relativity and 3-vectors. Special relativity and 4-vectors. Relativistic particle. Electromagnetism. Constant relativistic acceleration.
Spacetime: Equivalence principle. Spacetime as curved manifold. Tensors in curved spacetime. Rules for manipulating tensor indices.
The covariant derivative: How basis vectors change: the affine connection. Covariant derivative and parallel transport. Geodesic equations.
Spacetime curvature: Curvature and Riemann tensor. Riemann normal coordinates and the Bianchi identity. Information in Riemann.
The physics of curvature: Geodesic deviation. Tidal forces. Taking the Newtonian limit.
The power of symmetry, and Einstein's equations: Lie derivatives. Killing tensors. Maximally symmetric spacetimes. Einstein's equations.
Black hole basics: Birkhoff's theorem and the Schwarzschild solution. TOV equation for a star. Geodesics of Schwarzschild.
More advanced aspects of black holes: Causal structure of Schwarzschild. Reissner-Nordstrom black holes. Kerr black holes. The Penrose process.
Classic experimental tests of GR: Gravitational redshift. Planetary perihelion precession. Bending of light. Radar echoes. Geodesic precession of gyros. Accretion disks.
Gravitational waves: The wave equation for metric perturbations. Solving the linearized Einstein equations. Energy loss from gravitational radiation.

Communication

Here are my full contact details plus some helpful tips. Brief version:-

Scheduled office hours open to all students will be held online each week. Try this first if you have a question not already answered on the course website. Second option: email me to book a synchronous chat 1-on-1.
Emails are to be kept brief. I aim to respond to student e-mails within 24 hours. You can help speed up my response time by including the course code (PHY483) in the subject line of your message.
Note: if you ask for my academic help for any reason, that will not reduce my opinion of you. In fact, it is only likely to improve it.

Grading

Weightings

The grade you obtain in this course will be composed of

60% homeworks, composed of four 15% assignments due on R08Oct, R22Oct, R19Nov, R03Dec;
15% midterm oral assessment held during M02Nov-F06Nov;
20% final oral assessment held during F11Dec-S19Dec;
5% participation.

I recommend bookmarking this handy Calendar of Important Dates so that you do not accidentally miss important deadlines.

Details

Participation marks can be attained by attending synchronous tutorials if you are in a suitable timezone and can attend, or otherwise by attending office hours / 1-on-1 chats regularly. Please let me know ASAP if you are unable to regularly attend tutorials due to timezone constraints.

The homework assignments will involve mostly equation-centred problems fostering development of calculational skills (analytical and numerical), plus some qualitative problems fostering development of explanatory skills. You must clearly show the steps in your working in order to get full credit for calculational problems.

The oral exams will be 25 minutes long, beginning with a 5-minute check-in where you give me feedback about how the course is going for you, and then 20 minutes of conversational questions about lecture and homework material. Aids allowed: lecture notes.

Homework collaboration policy

You may discuss general concepts involved in calculational assignment problems with each other, but you must solve the details yourself and write up individual solutions in your own words. Problems involving you explaining concepts in written or video form must be done individually; I want to see your personal style shining through.

Lateness policy

Homeworks are due by 11:10am (the start of lecture) on the specified due dates. The lateness penalty is 5% per day up to a maximum of one week beyond the due date.

To help alleviate academic pressure at the busiest times of the semester, each student gets a bank account of seven Grace Days, which allows handing in homeworks late without penalty. You may use all seven on one assignment, or spread them out differently. My only rule is that you must inform the TA that you will be using a specific number of Grace Days at least 24 hours before the original due date.

Handing in

All homeworks must be submitted to the TA electronically for pandemic safety reasons. The TA's contact information will be posted in a Quercus announcement before the first tutorial. Quantitative parts must be clearly legible and in .pdf format (either from scanned handwriting or LaTeX), and qualitative parts can be submitted either in the style of a blog post as a .pdf or in a short .mp4 video. No other formats will be accepted.

Accessibility accommodations

Students with diverse learning styles and needs are welcome in this course. In particular, if you have a disability/health consideration that may require accommodations, please feel free to approach me as well as Accessibility Services. I am disabled myself, and very motivated to be decent to students managing physical and/or mental health disabilities. Here are some further important details on deadline extensions and accessibility accommodations.

Equity, Diversity, Inclusivity, and Excellence

At the University of Toronto, we strive to be an equitable and inclusive community, rich with diversity, protecting the human rights of all persons, and based upon understanding and mutual respect for the dignity and worth of every person. We seek to ensure to the greatest extent possible that all students enjoy the opportunity to participate as they see fit in the full range of activities that the University offers, and to achieve their full potential as members of the University community.

Our support for equity is grounded in an institution-wide commitment to achieving a working, teaching, and learning environment that is free of discrimination and harassment as defined in the Ontario Human Rights Code. In striving to become an equitable community, we will also work to eliminate, reduce or mitigate the adverse effects of any barriers to full participation in University life that we find, including physical, environmental, attitudinal, communication or technological.

Our teaching, scholarship and other activities take place in the context of a highly diverse society. Reflecting this diversity in our own community is uniquely valuable to the University as it contributes to the diversification of ideas and perspectives and thereby enriches our scholarship, teaching and other activities. We will proactively seek to increase diversity among our community members, and it is our aim to have a student body and teaching and administrative staffs that mirror the diversity of the pool of potential qualified applicants for those positions.

We believe that excellence flourishes in an environment that embraces the broadest range of people, that helps them to achieve their full potential, that facilitates the free expression of their diverse perspectives through respectful discourse, and in which high standards are maintained for students and staff alike. An equitable and inclusive learning environment creates the conditions for our student body to maximize their creativity and their contributions, thereby supporting excellence in all dimensions of the institution.

Academic Integrity

Academic integrity (AI) is fundamental to learning and scholarship at the University of Toronto. Participating honestly, respectfully, responsibly, and fairly in this academic community ensures that the U of T degree that you earn will be valued as a true indication of your individual academic achievement, and will continue to receive the respect and recognition it deserves.

Students are expected to know what constitutes AI: Familiarize yourself with the University of Toronto's Code of Behaviour on Academic Matters. It is the rule book for academic behaviour at the U of T. Potential offences include, but are not limited to:

In papers and assignments:: Using someone else's ideas or words without appropriate acknowledgement.; Copying material word-for-word from a source (including lecture and study group notes) and not placing the words within quotation marks.; Submitting your own work in more than one course without the permission of the instructor.; Making up sources or facts.; Including references to sources that you did not use.; Obtaining or providing unauthorized assistance on any assignment including (a) working in groups on assignments that are supposed to be individual work, (b) having someone rewrite or add material to your work while editing.; Lending your work to a classmate who submits it as his/her own without your permission.
On tests and exams:: Using or possessing any unauthorized aid, including a cell phone.; Looking at someone else's answers.; Letting someone else look at your answers.; Misrepresenting your identity.; Submitting an altered test for re-grading.
Misrepresentation:: Falsifying or altering any documentation required by the University, including doctor's notes.; Falsifying institutional documents or grades.

To remind you of these expectations, and help you avoid accidental offences, I will ask you to include a signed Academic Integrity Declaration with every assignment. If you do not include the statement, your work will not be graded. Please signal the fact that you have understood these Academic Integrity rules, and read all the other course webpages in detail, by sending me a funny cat/dog picture/video. Thank you for your attention in this regard.

The University of Toronto treats cases of academic misconduct very seriously. All suspected cases of academic dishonesty will be investigated following the procedures outlined in the Code. The consequences for academic misconduct can be severe, including a failure in the course and a notation on your transcript. If you have any questions about what is or is not permitted in this course, please do not hesitate to contact me. If you have questions about appropriate research and citation methods, seek out additional information from me, or from other available campus resources like the U of T Writing Website. If you are experiencing personal challenges that are having an impact on your academic work, please speak to me or seek the advice of your college registrar.

Notice of video recording and sharing

During pandemic conditions, I am teaching online-only to safeguard our lives and our health. Lectures in this course, including student participation, will be recorded on video, and will be available to students for viewing remotely in any timezone. Video links will be provided via announcements on Quercus a few hours after each class. Please note that course videos and materials belong to the instructor, the University, and/or other source depending on the specific facts of each situation, and are protected by copyright. In this course, you are permitted to download session videos and other materials provided via Quercus for your own academic use, but you should not copy, share, or use them for any other purpose without the explicit permission of the instructor.

Licence terms for course materials on this website

In the spirit of academic openness, I share all my course materials except class recordings on my own website for free, rather than securing them behind a tuition firewall. I started off by sharing lecture notes online soon after I began teaching at UofT in 2000, as an automatic accessibility accommodation so that students who could not take notes in class did not even have to ask for a note taker. I hope that sharing my course materials online is also useful to other UofT instructors wondering what I cover in my courses and how, and perhaps even to interested parties elsewhere. All my stuff is offered under a specific kind of licence which is less restrictive than traditional copyright but still has conditions: a Creative Commons Attribution-NonCommercial-NoDerivs Canada 2.5 licence. Please read the terms carefully.