Advanced Topics in Physics I - General Relativity (PHYS*4910)
Code and section: PHYS*4910*01
Term: Winter 2022
Instructor: Eric Poisson
This course offers an introduction to general relativity accessible to third-year and fourth-year physics students. The course focuses on the physics of weak-field and strong-field gravitation, as opposed to the mathematical formalism of general relativity. [Credit 0.50]
Class schedule and location
Monday and Wednesday, 11:30am to 12:50pm, MACN318.
There are no tutorials for this course.
Wednesday March 2, in class
To be determined.
Final exam weighting
Eric Poisson (email@example.com)
Office location and phone number
MacNaughton 452, 519-824-4120 x53653
There are no official office hours for this course. I am available for consultation over Zoom; please book an appointment over email.
I am very much an informal guy, and prefer to be addressed simply as “Eric”. I don’t particularly like being subjected to such pompous titles as Doctor, Professor, or Your Grace. My field of research is general relativity, including black holes and gravitational waves. For additional details, please consult my profile.
Graduate Teaching Assistant information
There is no TA for this course.
The following outline is tentative and might be subject to change during the semester.
- Spacetime physics. A review of special relativity. The four-dimensional spacetime formulation is introduced, and the laws of physics are formulated in flat spacetime.
- Newtonian gravity. A review of Newtonian gravitation. The laws of planetary motion are derived from a variational principle (principle of least action); this view plays an important role in the curved spacetime formulation of gravitation.
- General relativity. We begin our discussion of general relativity, in its weak-field (post-Newtonian) formulation. Newtonian gravity is reformulated in terms of warped time, and this picture is then improved by curving space as well. The curved spacetime formulation of gravitation predicts phenomena that are not contained in the Newtonian description: the gravitational redshift of photons, the deflection of light by a massive body and its associated time delay, and the advance of a Mercury's perihelion. We conclude with a brief discussion of the formal structure of Einstein's theory.
- Black holes. We describe, in the context of the exact theory of general relativity, the nature of curved spacetime around a black hole. We calculate the motion of bodies around black holes. And we reveal the existence of an event horizon: a place from which even light can no longer escape the hole's gravitational pull.
- Cosmology. The physics of the Universe as a whole. We show that general relativity predicts that the Universe should be expanding, and that this expansion comes with a decrease in temperature and a redshift of photons. We also show that under some circumstances, the expansion can be accelerating, a surprising feature that is observed today.
- Gravitational waves. Predicted long ago by Einstein, gravitational waves were finally discovered directly in 2015. Observations have now become routine, and they inform us of the dark side of the Universe: the collision of black holes and neutron stars. A general introduction to this topic will be given.
The interested student should have mastered Newtonian gravitation and special relativity (PHYS*2310), electromagnetism (PHYS*2330 and PHYS*2340), and Lagrangian mechanics (PHYS*3400).
There are no labs for this course.
There are no tutorials for this course.
The final mark for the course will be based on homework assignments (40%), a midterm exam (30%), and a final exam (30%). No other marking schemes will be considered.
A set of three homework assignments will be made available on Courselink, to be returned in class on the assigned due date. A penalty of 20% per day will be applied to any late assignment, and no assignment will be accepted after it has been marked. Special arrangements for late submission without penalty require a good reason and must be made well ahead of time.
The midterm and final exams will consist of problems to be solved, much like homework problems. These will be open-book exams, in the sense that you will be permitted to consult your course notes, your homework assignments, and the course’s official textbook. You will not, however, be allowed to consult any other source. Calculators may be required; only non-programmable pocket calculators are permitted. Personal communication or entertainment devices are not permitted during the exams.
(Not) Working with other students
All work submitted for grading in this course must be each individual student’s own work. While students are encouraged to share thoughts and ideas prior to writing up solutions to homework assignments, it is not acceptable to share assignment solutions. The assignments are not group projects, and it is important that you do not show your final written solutions to other students.
Completing assignments is an essential part of your preparation toward midterm and final exams. A serious attempt to do the work yourself, independently of others, will provide you with a very good preparation. Relying too much on others to provide pieces of solutions will give you a very poor preparation.
Please consult with Eric whenever the need arises. Do not wait too long before getting the help you need; it may be too late by then.
The recommended text for the course is
- Gravity: An Introduction to Einstein's General Relativity, by James B. Hartle (Pearson, 2002).
This is a wonderful text, which reflects the pedagogical strategy adopted in this course (emphasis on physical phenomena, not mathematical formalism). My lecture notes will not follow this text very closely, but the book is still highly recommended.
You may find it useful to also consult
- A First Course in General Relativity, by Bernard F. Schutz (Second Edition, Cambridge University Press, 2009).
This is very close rival to Hartle's book, with a very clear and accessible presentation of differential geometry, the mathematics behind curved spacetime.
See Course Evaluation (Marking schemes), above.
Course policy on group work
See Course Evaluation ((Not) working with other students), above.
Course policy on electronic devices and recording of lectures
What you do with your laptop, smart phone, tablet, etc, during lectures is your own business, so long as it does not create a distraction for your classmates or the instructor. (The instructor is easily distracted.) If such a distraction arises you will be asked to leave the classroom.
Electronic recording of classes is expressly forbidden without consent of the instructor. When recordings are permitted they are solely for the use of the authorized student and may not be reproduced, or transmitted to others, without the express written consent of the instructor.
As per university regulations, all students are required to check their e-mail account regularly: e-mail is the official route of communication between the University and its students.
When You Cannot Meet a Course Requirement
When you find yourself unable to meet an in-course requirement because of illness or compassionate reasons please advise the course instructor (or designated person, such as a teaching assistant) in writing, with your name, id#, and e-mail contact. The grounds for Academic Consideration are detailed in the Undergraduate and Graduate Calendars.
- Undergraduate Calendar - Academic Consideration and Appeals
- Graduate Calendar - Grounds for Academic Consideration
- Associate Diploma Calendar - Academic Consideration, Appeals and Petitions
Students will have until the last day of classes to drop courses without academic penalty. The deadline to drop two-semester courses will be the last day of classes in the second semester. This applies to all students (undergraduate, graduate and diploma) except for Doctor of Veterinary Medicine and Associate Diploma in Veterinary Technology (conventional and alternative delivery) students. The regulations and procedures for course registration are available in their respective Academic Calendars.
- Undergraduate Calendar - Dropping Courses
- Graduate Calendar - Registration Changes
- Associate Diploma Calendar - Dropping Courses
Copies of Out-of-class Assignments
Keep paper and/or other reliable back-up copies of all out-of-class assignments: you may be asked to resubmit work at any time.
The University promotes the full participation of students who experience disabilities in their academic programs. To that end, the provision of academic accommodation is a shared responsibility between the University and the student.
When accommodations are needed, the student is required to first register with Student Accessibility Services (SAS). Documentation to substantiate the existence of a disability is required; however, interim accommodations may be possible while that process is underway.
Accommodations are available for both permanent and temporary disabilities. It should be noted that common illnesses such as a cold or the flu do not constitute a disability.
Use of the SAS Exam Centre requires students to book their exams at least 7 days in advance and not later than the 40th Class Day.
For Guelph students, information can be found on the SAS website
The University of Guelph is committed to upholding the highest standards of academic integrity, and it is the responsibility of all members of the University community-faculty, staff, and students-to be aware of what constitutes academic misconduct and to do as much as possible to prevent academic offences from occurring. University of Guelph students have the responsibility of abiding by the University's policy on academic misconduct regardless of their location of study; faculty, staff, and students have the responsibility of supporting an environment that encourages academic integrity. Students need to remain aware that instructors have access to and the right to use electronic and other means of detection.
Please note: Whether or not a student intended to commit academic misconduct is not relevant for a finding of guilt. Hurried or careless submission of assignments does not excuse students from responsibility for verifying the academic integrity of their work before submitting it. Students who are in any doubt as to whether an action on their part could be construed as an academic offence should consult with a faculty member or faculty advisor.
- Undergraduate Calendar - Academic Misconduct
- Graduate Calendar - Academic Misconduct
Recording of Materials
Presentations that are made in relation to course work - including lectures - cannot be recorded or copied without the permission of the presenter, whether the instructor, a student, or guest lecturer. Material recorded with permission is restricted to use for that course unless further permission is granted.
The Academic Calendars are the source of information about the University of Guelph’s procedures, policies, and regulations that apply to undergraduate, graduate, and diploma programs.