P208, Win 2017
General Relativity
Instructor: Prof. Flip Tanedo, , Physics 3054
Textbook:
An Introduction to Einstein's General Relativity, Hartle (Pearson 2003).
| Lec: | TR 5:10-6:30pm | Room: | Phy 2104 |
| Dis: | n/a | Room: | n/a |
| Final: | none | Room: | none |
Grades and course announcements via iLearn.
This is a graduate course in general relativity. We focus on the physics of relativity and understanding relativistic phenomena. Topics will include the Einstein equation, black holes, and gravitational radiation.
Due to the brevity of the 10-week quarter and the fact that this is an advanced course, students are expected to do signficant reading and to bring their questions to class and discussions.
Assignments
Homework is due on Tuesdays. LaTeX files (no figures) are available for those who would like to typeset a clean solution set in exchange for extra credit and their name on the solution set.
Homework 1, Due 17 January: Special Relativity (tex)
Homework 2, Due 31 January: Adding Velocities and Equivalence Principle (tex)
Homework 3, Due 7 February: Curved Space (tex)
Homework 4, Due 14 February: Schwarzschild (tex)
Homework 5, Due 21 February: Killing Fields and Black Holes (tex)
Homework 6, Due 2 March: Maximal Extension, Conformal Diagrams (tex)
Homework 7, Due 7 March: Einstein Equation (tex)
Lecture Notes
These notes are provided as is and are riddled with errors. Use them as a guide for what we covered in class. Lectures are complementary to the assigned reading; they are most meaningful if you do the reading ahead of the lectures.
Lec 1, 10 January: Overview, Review of Special Relativity, Diagnostic
Lec 2, 12 January: Minkowski Space, our plan for the course
Lec 3, 17 January: Intelligent Falling: Equivalence Principle
Lec 4, 19 January: Affine Connection, Covariant Derivative
Lec 5, 24 January: Newtonian Limit, gravitaitonal time dilation, geodesics
Lec 6, 26 January: Riemann Tensor, Intrinsic/Extrinsic, Lie Derivative
Lec 7, 31 January: Riemann Tensor Redux, Rotationally Invariant Spacetime
Lec 8, 7 February: Intro to Schwarzschild
Lec 9, 9 February: Killing Fields, Lie Derivative
Lec 10, 14 February: Schwarzschild black hole coordinates
Lec 11, 16 February: Maximal extension of Schwarzschild, conformal diagrams
Lec 12, 23 February: Einstein Equation the Easy Way
Lec 13, 28 February: Einstein Equation the Hard Way
Lec 14, 2 March: Understanding Einstein's Equation
Lec 15, 7 March: A Wave Equation in Gravity
Lec 16, 9 March: Gravitational Waves
Lec 17, 14 March: Differential Forms
Lec 18, 16 March: Integrating Differential Forms
Useful Links
Some recent articles that may be useful.
- "Teaching General Relativity", R. Wald.
- The General Relativity Tutorial, J. Baez (UCR). A summary of general relativity in a readable style. (See also "The Meaning of Einstein's Equation")
- "EPFL Lectures on General Relativity as a Quantum Field Theory," by Donoghue et al. The first section shows the connection between gravity and the gauge theories that particle physicists like.
- Most images of black holes are illustrations. Here's what our telescopes actually capture. , B. Resnick for Vox.
- Signal Processing with GW150914 Open Data , LIGO tutorial for working with its open data.
- Gravitational Wave Resources , Marc Favata. A useful compendium of resources. See also his gravitational wave outreach page.
- Sounds of Spacetime
- "The Foundation of the General Theory of Relativity" (German, 1916), Albert Einstein. Also ""On Gravitational Waves," by Einstein and Rosen (1937).
Useful References
Students are strongly encouraged to use complementary materials, especially those that fit best with their own background and interests. Here are a few books that I like.
- Spacetime and Geometry, S. Carroll. An excellent introduction to the subject for theorists based closely on these lecture notes. Develops Riemannian geometry ahead of physics applications, which may appeal to the mathematically inclined. (If so, don't forget to read the appendices.)
- Einstein Gravity in a Nutshell , A. Zee. Tony Zee's textbooks are a pure joy to read and are full of physics insights. They're conversational and ideally suited for self study.
- Part III General Relativity , H. Reall. Lectures from the General Relativity course of the Part III of the Maths Tripos in Cambridge. These lectures focus primarily on a development of Reimannian geometry for relativity. See also the lecture notes on black holes.
- Gravitation , Misner, Thorne, and Wheeler. The usual joke about this book is that it is so heavy that it lets you study general relativity experimentally. It's a comprehensive tome, but perhaps too comprehensive to be very useful for an introductory course.
- A First Course in General Relativity , B. Schutz. This was one of the runners-up to be the course textbook. It has a similar approach to Hartle in front-loading the physics ahead of the mathematics.
- Gravitation and Cosmology , S. Weinberg. This may be out of print; it's an old standard with lots of physical intuition and applications without compromising the mathematics. There's a lot in here, though, so you may need to jump around and skip chapters strategically.
Collaboration & Academic Integrity
I strongly encourage you to work collaboratively and learn from one another. I don't anticipate grading to be an issue in an advanced course like this. However, do I expect everyone to abide by the UCR code of academic integrity. Practically: work on problems collaboratively, but write up your own work independently. If you find other resources or papers relevant for your problems, cite them in your work.