ANNOUNCEMENTS
MTH 437/537 — Spring 2009

6/10/09

The exams are graded, and (most) grades have been submitted.

I should be in my office Friday morning if you want to pick up your exam.

6/7/09

I expect to be in my office Monday from roughly 10—11:45 AM and again from roughly 1—3 PM, with similar hours Tuesday morning (until noon). There is a good chance I'll be there before/after these times as well, and other times can be arranged; email me to make an appointment.

6/3/09

The figure I showed today, with the classification of FRW solutions, can be found here.

6/2/09

Latest news from the GR community:

A newly revised Mathematica package for doing curvature computations is available here.

Some recent interviews with well-known scientists about black holes can be found here.

5/27/09

We will have a takehome final, which is tentatively scheduled to be given out in class on Friday, 6/5, and will likely be due at noon on Tuesday, 6/9.

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

5/20/09

My notes on GRTensor for computations in relativity have been revised to include the updates below.

Please let me know of any problems you have when attempting to follow these instructions.

5/19/09

Here are some updates on the use of Maple and GRTensor:

• The (default) Java worksheet interface to Maple requires a double-quote rather than a backquote when entering path names. Thus, on COSINe machines, the path should be entered as
        libname:=libname,"/home/math/tevian/GRtensor/lib":
• From campus machines running Maple and Windows, such as those in the MLC, you should be able to load GRTensor by first adding poole as a network place, then entering (note the repeated backslashes):
        libname:=libname,"\\\\poole\\ClassFolders\\Math-Dray\\GRtensor\\lib":
  (You may need to replace poole by its FQDN, namely poole.scf.oregonstate.edu.)
• Be warned that GRTensor by default provides coordinate basis components, even if you specify an orthonormal basis, e.g. by using the "non-holonomic basis" option to makeg. In order to get the components with respect to the basis, you must enter something like
        grcalc(R(bup,bdn,bdn,bdn)):grdisplay(R(bup,bdn,bdn,bdn));
  where the "b" stands for "basis".
• I've saved the best for last: The makeg command does not work well with the Java worksheet interface, which opens a blank window for you to answer its questions, but doesn't then tell you what the questions are! Yes, you can enter the necessary information into these windows, but you'll need to figure out what the questions are (e.g. by first using another interface). I do not yet know how to disable this "feature", other than recommending the use of another Maple interface; the "Classic Worksheet" or "Command Line" interfaces should both work fine.

5/18/09

My MW office hours this week should be regarded as canceled.

There's a good chance I will be there by 11:15 on M and before 11 on W, but this is not definite. Please contact me to arrange an alternate time if needed.

5/15/09

You may rework and resubmit your midterm.

• You may use any references you wish, but please do not seek help from anyone other than me. You should however feel free to consult with me prior to actual resubmission.
• The maximum number of additional points available is half of the points you did not already earn. (If you already received more than half credit on a problem, it's not worth resubmitting it.)
• The standard for earning additional points will be higher than on the midterm itself — it's up to you to present your argument clearly.
• Please resubmit your work as soon as possible, and no later than Friday, 5/22. Please be sure to include your original midterm with your resubmission.

5/13/09

Jeff Hazboun will give a talk today at 4 PM in Weniger 304 on his work with Schwarzschild black holes.

Further details are available here.

5/12/09

As announced in class yesterday, I will not be in my office during the day today. I will however come in briefly later in the day, tentatively from 5:30–6:30 PM. (This is an update from the originally posted time.)

• It wouldn't hurt to let me know by email that you are coming — the above times should not be taken as exact, but I will do my best to wait for those who have contacted me.
• Don't hesitate to send questions via email — I should have email access briefly this afternoon, and will also be checking my email later in the evening.

I will hold extended office hours tomorrow (Wednesday) morning, from 9:30 9:00–11:45 AM.

5/7/09

The midterm will cover everything discussed in class through Friday, 5/8.

• Important topics are special relativity (hyperbola geometry), the Schwarzschild black hole, and geodesics.
• Suggested review (read or skim): Gravity: §2–§4, §8–§9, §12; EBH: §2–§4; my notes.

Copies of the slides from a talk quite similar to my colloquium are available here.

5/5/09

My office hours tomorrow will be slightly earlier than usual, namely from 9:30–10:45 AM.

5/4/09

We will have a takehome midterm, which will be given out in class on Monday, 5/11, and will be due no later than the beginning of class on Wednesday, 5/13.

4/29/09

There's not much material in our text about accelerating observers in Minkowski space.

You might want to take a look at this Wikipedia page.

4/27/09

You may want to skim §4 of EBH, which has an extensive discussion of orbits in the Schwarzschild spacetime, making extensive use of the potential diagram briefly discussed in class.

4/23/09

There is a typo in (9.32) on page 195 of Gravity:

The LHS should read E_Newt (1 + E_Newt ⁄ 2mc²).

4/22/09

The geodesics of the Schwarzschild spacetime are discussed in §9.4 of Gravity.

Glance through this section if you are having trouble with the homework.

4/21/09

I will give the Physics Department Colloquium next week on special relativity, using the geometric language we discussed at the beginning of the term. Further details are available here.

4/15/09

Please note that next week's homework is not due until Friday.

We will not discuss geodesics in the Schwarzschild spacetime until Wednesday, so you may want to postpone working on the first two problems until then.
(The last problem does not require knowledge of geodesics.)

4/10/09

The room for our rescheduled class meetings (W 4/15 & W 4/22 @ 4 PM) will indeed be in our regular classroom (Wngr 275).

4/8/09

As discussed in class today, we will reschedule a couple of class meetings:

We will not meet Friday 4/17 or Monday 4/20.

We will meet twice on Wednesday 4/15 and Wednesday 4/22, both at our normal time and at 4 PM.

The room for the rescheduled meetings will be announced later.

4/3/09

The video I showed in class today 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.

4/2/09

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.

4/1/09

A simplified introduction to differential forms can be found here.

Further details about the Hodge dual can be found here.

Further details about connections can be found here.

Further details about curvature can be found here.

You may also want to look at either or both of the textbooks used for MTH 434.

3/25/09

There is a regional conference in general relativity this weekend at the University of Oregon. Yes, this is an advanced research meeting, but you might find it of interest to see what work is currently being done. Further information is available here.

Contact me if you're looking for a ride.

3/24/09

Textbooks were ordered late, but should arrive next week.

Note the corrected information on the course home page regarding the officially required text, as well as the additional information on this page

We will discuss textbooks further on the first day of class.

2/19/09

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

• 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.
• Spacetime puts the detailed discussion of tensor analysis first, then provides a careful, clear discussion of the physics.

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

• If you are seriously interested in the physics of general relativity, Gravity is worth having.
• If you are primarily interested in the mathematics, you may find Spacetime easier to read.
• However, we will use the language of differential forms wherever we can, which is not extensively covered in any of these books. We will therefore take a somewhat more sophisticated approach than EBH, while trying to avoid at least some of the tensor analysis in Gravity or Spacetime.

In short, none of these books is perfect, but all are valuable resources. You should be able to manage with any of them, so long as you are prepared to refer to the others in the library when needed.

2/18/09

There is some possibility of changing the course time.

If you are considering taking this class, and would prefer a different time, please contact me.
(It would be useful to know the times when you could not take the course.)