ANNOUNCEMENTS
MTH 437/537 — Spring 2007

6/14/07

The exams have been graded, and course grades submitted.

Course grades should be available online tomorrow.

Exams can be picked up from me at any mutually convenient time, including next term.

6/11/07

I expect to be in my office today (Monday) from 9:30–11:30, and tomorrow (Tuesday) from 9:30–12:00.

6/10/07

I expect to be in my office after lunch today (Sunday).

I should get there by 1:30, and will stay as long as necessary — but will feel free to leave after an hour or so if nobody is waiting. You may wish to phone or email me to check whether I'm (still) there.

6/9/07

Due to possible email problems on the College of Science server, I recommend that you send messages to my ONID account (userid: drayt).

I will confirm receipt of all messages.

Update: The problem has been tracked down; mail should not have been affected.

6/1/07

One student in the class found this website for a course in relativity, and found it quite helpful.

5/30/07

The final in this class will be a take-home exam.

• Expect the exam to be comparable to, but somewhat longer than, a typical homework assignment.
• I plan to hand out the exam on Friday, 6/8.
• The exam will be due at noon on Monday, 6/11 Tuesday, 6/12.

If these arrangements will cause difficulties with your schedule, let me know as soon as possible!

5/27/07

I have corrected a minor typo in the code given for the Schwarzschild metric in my notes on SHEEP.

5/20/07

I will not be in my office Wednesday morning as scheduled. Feel free to look for me at other times, including tomorrow morning (Tuesday) after 10, or Friday after class.

5/19/07

The book's website has some useful supplementary material, including some detailed computations omitted from the text, as well as Mathematica notebooks for doing other computations, including curvature.

5/14/07

A copy of my article on the twin paradox on the cylinder will be posted outside my office:

The Twin Paradox Revisited,
Tevian Dray, Am. J. Phys. 58, 822–825 (1990).

This article is also available (but not on reserve) in the library.

5/9/07

I expect to be in my office tomorrow from roughly 1–2 PM. Other times are possible if arranged in advance.

5/4/07

The midterm will be in class next Monday, 5/7.

• The exam is closed book.
• The exam will cover everything discussed in class through Wednesday, 5/2.
• Important topics are special relativity (hyperbola geometry), the Schwarzschild black hole, and geodesics.

4/27/07

You can find a further discussion of the Painlevé-Gullstrand coordinates introduced in class today here.

4/26/07

To clarify the last computation in yesterday's lecture, there are three notions of time involved:

• Far-away time t is that seen by an observer far from the black hole; this is just the Schwarzschild time coordinate. Far-away time is also called bookkeeper time in EBH, as it does not correspond to actual measurements (except those made far away).
• Wristwatch time τ (tau) is the time which actually elapses for each observer. It can be measured by any observer as the "length" of the given trajectory, obtained by integrating the line element.
• Shell time is the time measured by an observer standing on a shell of fixed radius.
  (EBH writes this as t_shell, but there is in fact no such coordinate; shell time is obtained by integrating the line element along a path with r,θ,φ fixed.)

Be careful to distinguish between wristwatch time and shell time; you may find it helpful to draw a triangle and use the Pythagorean Theorem. The computations done in class were (supposed to be) dr/dt and dr_shell/dt_shell.

Note that r_shell is a reasonable coordinate, which we have often called s, since it is possible to do the integral which relates dr and ds.

4/19/07

I have posted some notes on the geodesic equation using the approach covered this week in class.

4/17/07

The first homework problem is supposed to be quite easy!

If using an approximation, think about whether it is reasonable. What quantity is small? How small is it?

4/13/07

Strange but true: The 13th of the month is more likely to be a Friday than any other day of the week!

Give up? Further information is available here.

4/11/07

This week's homework assignment is about radial measurements in the Schwarzschild geometry, which we will discuss in more detail on Monday.

4/9/07

I will be out of town this Friday, 4/13/07. I will arrange to show (excerpts from) two videos on relativity, one of which is also available online, as described in an earlier announcement. Attendance is optional.

4/8/07

The earliest known spacetime diagram is reproduced in Box 4.2 of Gravity.

4/6/07

You may find it helpful to start the first homework problem by considering 2 dimensions rather than 4.

(The broken link to my notes has been fixed.)

4/5/07

A nice video on special relativity can be found here.

The above link is a Windows Media file, which you may need to open directly in a media player, not a browser. You can also try this URL, or go to this site (registration required) and scroll down to Program 42 (The Lorentz Transformation).

The spacetime animations starting after roughly 8, 11½, and 19½ minutes are especially good.

4/4/07

The slides I used in class today can be found here.

4/3/07

When thinking about paradoxes in special relativity, you may wish to bear in mind Wheeler's First Moral Principle (from the book Spacetime Physics by the authors of EBH):

Never make a calculation until you know the answer.

3/17/07

A "review" of curvature can be found here.

You are not expected to know everything presented in these notes. The first part of the course will not in fact discuss curvature at all. However, curvature is the key geometric idea behind Einstein's equation, and you will be expected to understand curvature calculations later in the course. The classroom presentation will emphasize the language of differential forms, but it should be enough to be able to use — or at least believe — any one method for computing curvature, such as those presented in §3.

2/21/07

The level of this course will be somewhere between that of the two texts, henceforth referred to as EBH (Taylor and Wheeler) and Gravity (Hartle).

• EBH uses only basic calculus to manipulate line elements, and only discusses black holes, but does so in great detail.
• Gravity begins essentially the same way, starting from a given line element to discuss applications, including both black holes and other topics. This is followed by a full treatment of tensor calculus, including a derivation of Einstein's equation.

We will cover more material than EBH, but we will stop short of the full tensor treatment in (the back of) Gravity. We will also cover some of the material on black holes from EBH which is not in Gravity.

• If you are seriously interested in the physics of general relativity, Gravity is worth having.
• If you have a copy of Gravity, you should be able to manage without EBH, although some of the homework may come from there.
• If you are primarily interested in the mathematics of general relativity, you can go either way. We will use differential forms wherever we can, and will therefore take a somewhat more sophisticated approach than EBH, while trying to avoid at least some of the tensor analysis in Gravity (which is also in Bishop & Goldberg).

In short, neither book is perfect, but both are valuable resources.