PHY483F

Relativity Theory I (2017-18) -- 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 tensor index gymnastics.
The covariant derivative
Christoffel connection. Covariant derivative and parallel transport. Geodesic equation. Noncoordinate bases, spin connection.
Spacetime curvature
Curvature and Riemann tensor. Riemann normal coordinates and the Bianchi identity. Information in Riemann.
The physics of curvature
Geodesic equation. Tidal forces. Geodesic congruences and the Raychaudhuri equation.
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. Gravitational redshift and the Pound-Rebka experiment. Geodesics of Schwarzschild.
More advanced aspects of black holes [if time permits]
Causal structure of black holes. Charged black holes. Rotating black holes. Black hole thermodynamics and the information paradox.
Experimental successes of GR
Planetary perihelion precession and bending of light. Radar echoes and geodesic precession of gyros. Gravitational radiation.
Upgrading Newton's gravity to Einstein's
Ricci, Weyl and Einstein tensors. Tensor densities and integration. Energy-momentum tensor and relativistic scalar gravity. Building tensor gravity with the right Newtonian limit.
Deriving Einstein's equations from an action principle
The action principle for Einstein's GR. Simple examples of energy-momentum tensors.
Cosmology
A brief introduction to FRW cosmological models of the evolution of the universe.

Grading

The grade you obtain in this course will be calculated from

The reason why tutorials count towards your final grade is to provide an incentive to attend tutorials as well as lectures. In previous years, we found a strong correlation between attending tutorials and higher final grades. Please plan on attending both lectures and tutorials on a regular basis.

Homework collaboration policy: students may discuss generalities of the assignment problems together, but must write up individual solutions in their own words.

Lateness policy: homeworks have a grace period of one day, the lateness penalty after that is 5% per day up to a maximum of one week beyond the due date, and all non-medical extensions must be requested at least one week before the due date. See also the calendar of events and more details on deadline extensions and accessibility accommodations.

Writing requirements

Please do NOT hand in any graded work handwritten in pencil - homeworks, midterms, or final exams. Pencil can later be erased and changed during a grading dispute. If you write in pencil, you will be barred from asking for a regrade. Another reason to avoid pencil is that pencil written assignments are typically hard to read under artificial light, and their scans often have insufficient contrast. Please handwrite in black or blue pen (avoid red, for obvious reasons). Crossouts are fine, as long as they are clearly marked.

Accessibility is something I take seriously, because I am a person with disabilities myself. It is the main reason why I provide lecture notes online for all my courses. So if you prefer to prepare your homework assignments in LaTeX, that is just as good as handwriting from my perspective. Regardless of the format you use, you must show all the key steps in your working in order to get full credit for a problem.

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.

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.