Mathematics 489, Section 500, Fall, 2009
Tensors and General Relativity
Last updated Mon 21 Dec 09
Announcements (reverse chronological order)
- Dec 21: The final exam key
is posted below.
Please study at least the multiple-choice questions. I expected better
results there.
- Dec 17: Final exam and course grades are now in Vista.
Curve? Yes, so violent you don't really want to know.
(I think the course achieved its aims for most of you.)
I will try to post at least a partial final
exam solution set later this week.
I was disappointed in the results of the tensor index manipulation
problem. It was essentially the same as Qu. 5 of the Fall 2005 final;
please read that solution. On the other hand, you did well on the
open-ended question about static solutions.
- Dec 4: Announcement of next
Math Club
Meeting (Dec 8) (movie)
- Nov 4: Test announcement for
Nov 11 and 13
- Oct 25: (a) Test key is posted below, and grades have been
brought up to date in Vista. (b) Some notes on counting degrees of
freedom have been added below (under "Supplementary material").
- Sep 27: No office hour on Monday, Sep 28.
(I need to attend a Ph.D. oral exam.)
- Sep 16: Special procedures for week of Sep 21-25:
Prof. Yasskin will handle the class in my absence.
- Start work on the electromagnetism paper. Read the instructions
all the way to the end! Dr. Yasskin will answer questions about the
assignment on Friday.
- Read Chapter 4 "superficially" (see below).
- Read Sec. 5.1.
- There will be no written homework on Chapters 3 and 4.
- In Week 6 (starting Sep 28) I'll be back and we will work hard on the
rest of Chapter 5!
- Sep 1: Undergraduate Research
Scholars announcement
- Aug 30: Announcement of Sep 16 meeting on
How to Find and Compete for Graduate Fellowships
Course handout
._._.
Please see
my home page for up-to-date office hours.
Track your grades on Blackboard
Vista.
Electromagnetism paper ._._.
Here's the TeX file,
in case you want to import some of the questions into your own document.
It is in Plain TeX and uses
the vanilla macros.
(LaTeX users will need to make some changes.)
Homework exercises (These are not to be turned in except as
announced. Uncollected problems, or questions inspired by them, may show
up later on exams.)
- Chapter 1: 3, 5, 13, 14, 15, 18, 19 (Turn in 18 and 19 on Sep 9,
along with any thoughts on the following for extra credit.)
Also: Make a list of the assumptions made (explicitly or
implicitly) in the "proof" in Sec. 1.6. (An example of the
sort
of issue I have in mind here is this: In Sec. 1.5, p. 7, we
read
that "the event R on the t axis must be as
far from the origin as event E." Does this tacitly
assume an invariance under time reversal?)
- Chapter 2: 12, 13, 16, 19, 21, 22, 24, 30 (Turn in 19 and 24 on Sep
16. It may help to do 21 before 19.)
- Chapter 3: 4, 6, 9, 13, 16, 21 (No written homework.)
- Chapter 4: None (We will not "cover" this chapter, but you will want
to read it at least superficially to assure continuity with the later
chapters.)
- Chapter 5: 2, 7, 8, 11, 12, 13, 20, 22 (No written homework.)
- Chapter 6: 7, 9, 13, 18, 23, 25, 32, 33
Also: Calculate the Christoffel symbols for the Robertson-Walker
metric (12.13). (Work in pairs! One of you should use the geodesic
Lagrangian method (see notes, pp. 41-42), and the other should check the
results with eq. (5.75). (Trade jobs halfway through.) Turn in one
paper per pair on Oct 23.)
- Chapter 7: 2, 7 [omit (iii)] , 10 (See next line for instructions.
Hint on
10(b): There are 4 types of symmetries: space translations, time
translation, rotations, Lorentz boosts.)
- Chapter 8: 4, 5, 9, 18 (From Chapters 7 and 8, turn in only
Exercises 7.7, 7.10, and 8.18. These are "extra credit" -- that is, I
don't
expect most of you to do them, or to complete them. I'll accept papers
any time before the end of classes (Monday, 7 Dec).)
- Chapter 12: 1, 4, 8, 20, 21
Also: For the Robertson-Walker metric, calculate the Riemann tensor
(20 independent components), Ricci tensor, Ricci curvature scalar, and
Einstein tensor.
Check that the last obeys the conservation law (contracted Bianchi
identity). (Work in teams and turn in one paper per team on Nov 18.)
- to be continued
Test solutions
Supplementary material
Old course home pages:
Spring 2008 ._. Fall 2005
Go to home pages:
Fulling ._._.
Calclab ._._.
Math Dept ._._.
University
e-mail: fulling@math.tamu.edu