Instructor: Moshe Rozali, e-mail: rozali@phas.ubc.ca (TA email: qingdi@phas.ubc.ca).
Lectures: Mondays, Wednesdays and Fridays, 1-2 in Hebb 12.
Office hours: Mondays 3-4, or by appointment (my office is in Hennings 412).
Textbook: James Hartle: Gravity, an introduction to Einstein’s General Relativity (available at the bookstore).
Everything I will cover is based on this book, I will follow roughly the outline of the book, but with a lot of skipping, fast forwarding and back-tracking.
Schedule changes: Classes on Friday March 16 and Wednesday March 21 are cancelled. The classes on March 12,14,19 will be taught by Mark van Raamsdonk.
Midterm: The midterm on March 5 will cover all the material covered in class or homework up to the end of chapter 8, that is including geodesics but not the more recent material about the Schwartzschild solution.
There are no books or notes allowed, I'll supply all the formulas needed (on the exam itself, or in class in response to questions) and you are allowed one page of formulas.
Most of the text mentioned here are more advanced, but you can consult them for alternative explanations of the material covered in class. They are all different, and I’ll try to give a flavor of the various differences. I list them in the order of my personal preference.
Spacetime and Geometry, Sean Carroll: The best next level text, and my recommendation for those who want an additional text to consult. Since it is more advanced, it covers much more of the math (differential geometry) needed to appreciate Einstein’s equations. It does have a lot of interesting physics as well.
Gravitation and Geometry, Steven Weinberg: Famously, much less emphasis on the geometrical apparatus, and more on physical applications. Thorough and authoritative.
First course in General Relativity, Bernard Schutz: Solid text covering the basics, doesn’t go much beyond what Hartle does.
General Relativity, Robert Wald: The standard text for the mathematically inclined, dense but worth unpacking. Most of the material is beyond what we'll cover in this course.
Gravitation, Misner Thorne and Wheeler: The standard text of the previous generation. Contains much more than other books, but is best used as reference book. With some editing could have probably made 3 good (and very different) textbooks, but combined together it is somewhat incoherent to my taste.
The first few chapters of Hartle are beautifully written, and describe interesting gravitational phenomena. I will cover them is somewhat different order, and will skip thew more qualitative parts. I recommend reading the text itself to supplement the lectures.
The first part of the course will cover the basics:
1. Special Relativity and dynamics of particles moving in flat spacetime.
2. The gravitational field, analogy with the electromagnetic field, and .the differences. The principle of equivalence.
3. General coordinate invariance, the principle of general relativity and the geometrical apparatus.
These subjects are covered in the first 5 chapters of the text. I am assuming some familiarity with the material, so I will emphasize the conceptual underpinning of the subject, and worry less about the math at that point.
Once we have established the usefulness of geometry in describing relativistic gravity, we will turn into more detailed description of the geometry needed. This is described in chapters 6-8 of the text, and is concerned with the basic machinery needed to describe the motion of a particle in a given gravitational field. We will learn how the spacetime geometry of special relativity (itself a generalization of Euclidean geometry), is generalized for curved spacetimes. Once we have that, we will find a few ways to visualize the curved spacetime, to find the way objects move in a given geometry.
After acquiring this machinery we are ready for interesting applications. Depending on the time left, there could be a few: black holes, gravitational waves and cosmology. More details on that part of the course will be given once it is clear how much can be covered.
Problem sets 25%.
In-class mid-term 25%.
Final exam 50%.
Homework will be given once a week (on Wednesdays), and will be due a week later in class or by 4:00pm (they can be left in my office, or under my door if I'm not there). Late homework are accepted up to one week late for half credit.
You are welcome to discuss the problems with the other students, but the submitted assignments must be your own work.
Please try to resolve grading issues for assignments with the TA first. Contact me if there are still unresolved issues.
Homework #1: Chapter 3, problems 1,2,5, due Wednesday January 25, solutions of homework1
Homework #2: Chapter 4, Problems, 3, 12, 17, due Wednesday February 1, solutions of homework2
Homework #3, Chapter 5, Problems 2,4,6, due Wednesday February 8, Solutions.
Homework #4, Chapter 7, Problems 5,7,14, due Wedneday February 15, Solutions.
Homework #5, Chapter 8, Problems 4, 12, due Wednesday February 29, Solutions.
Homework #6, Chapter 9, Problems 6,15, due Wednesday March 14, Solutions.
Homework #7, due Friday March 23. solutions of homework7
Homework #8, Chapter 7 problem 22 and Chapter 9 problems 3,8, due Wednesday April , solutions.
Midterm solutions: midterm