ANNOUNCEMENTS
MTH 437/537 — Spring 2011

6/8/11

The exams have been graded.

• Course grades have been uploaded and should be available online tomorrow.
• You can pick up your exam from me starting next week — email me to set up a time if you're not able to catch me in my office.
• Exam scores were good; the average was 65/80, with a handful of near perfect papers.
• A common pitfall was inadvertently giving Minkowski space as an example in Problem 3.
• I was also a bit surprised by how many folks failed to notice that sin²ψ/(1−cos²ψ)=1 …

6/5/11

I expect to be in my office tomorrow (Monday) no later than 10 AM 9:30 AM, and probably somewhat earlier. Except for lunch, I should be there until at least 2 PM.

Somewhat earlier or later times should be possible if necessary; let me know.

I will be in my office on Tuesday no later than 9:30 AM, and will stay until noon.

6/4/11

Kidder Hall appears to be locked!

Either call my office (737-5159), email me, or go to the north side of the building and yell, and I'll let you in.

6/3/11

Final Exam Typo: The last dy² in Problem 3 should be dz².

Also note that "dot" is not a derivative with respect to t in Problem 1 (although it is in Problems 2 and 4).

I should be in my office today until at least 2 PM, and tomorrow, Saturday 6/4, from roughly 11 AM – 12:30 PM.

(Weather permitting, I will then go to the Physics Dept Picnic; yes, you can ask me questions there.)

I also expect to be in my office most of the day Monday (6/6), and all morning Tuesday (6/7).

Feel free to email me with questions, and/or to set up an appointment.

6/2/11

Instructions on using the newer DifferentialGeometry package, available in Maple 14 (and possibly Maple 13), to compute curvature tensors can be found here

6/1/11

There is a bug in GRTensor:

In some cases, rot(bup,bdn,bdn) differs by a sign from the components of the connection 1-forms.

Loosely speaking, this only affects components whose indices contain precisely one "t". More precisely, the components Γⁱ_jk of the connection one forms ωⁱ_j = Γⁱ_jk σ^k are in fact given by rot(bdn,bup,bup) …

5/29/11

A PDF copy of the class notes can be downloaded here.

5/27/11

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

5/25/11

Several students are having trouble printing out their GRTensor worksheets. If this affects you, please try the following:

• Make sure to start a fresh Maple session, e.g. by using the command restart:.
• Make sure you are using the Classic Worksheet interface, not the (newer) Java-based interface.
• Try a different version of Maple. (The machines in Weniger should have more than one.)
• Try a different computer. (Maple can be found in Weniger 304F, in the MLC, and elsewhere.)

If none of the above steps helps, you should email a copy of your worksheet to me, along with details about the location of the computer and the Maple version.

Further information will be posted here as it becomes available.

(If you are not having difficulty, it would help for me to know the details (machine location and Maple version), so that I can try to track down the problem.

5/24/11

There should be time next week to discuss one or more advanced topics in relativity. Possibilities include more detailed discussion of cosmological models, and black holes with additional structure, such as charge and angular momentum.

Suggestions and comments are welcome.

5/22/11

We will have a takehome final, which is tentatively scheduled to be given out in class on Friday, 6/3, and will likely be due at noon on Tuesday, 6/14.

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

5/14/11

There will be an extra class meeting on Monday, 5/23, from 5:30–6:20 PM in Weniger 304.

5/13/11

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.

5/12/11

There will be no class the week of 5/16–20.

5/11/11

I will be speaking about my research later today (12 PM in Gilkey 113) in the Math Dept graduate seminar. About symmetry groups, not relativity. Further details are available here.

5/10/11

CLASSI should now be working on the ONID shell server shell.onid.oregonstate.edu (as well as on frontend.science.oregonstate.edu).

For ONID, replace "~tevian" with "~drayt" in the instructions, which have been updated.

When using GRTensor, use rot(bup,bdn,bdn) rather than Chr(bdn,bdn,bup) to compute the connection.

Again, the instructions have been updated.

5/6/11

There will be an extra class meeting on Monday, 5/9, from 5:30–6:20 PM in Weniger 304.

5/5/11

Some notes on the use of computer algebra in relativity can be found here.

Printouts of sample sessions are available for GRTensor and CLASSI.

An older version of these notes, including instructions for coordinate-based computations, can be found here and here.

5/3/11

The rescheduled classes are tentatively scheduled for Monday 5/9 and Monday 5/23, both at 5:30 PM.

Please let me know of any conflicts as soon as possible.

4/28/11

Due to conference travel, I will again be out of town for three class periods this term. I would like to reschedule those classes if possible.

Will Mondays at 5:30 PM work again? Not 5/16, on which I believe there is a Paradigms final, but how about 5/9 and 5/23? That still leaves us one day short...

4/27/11

I have added footnotes to §1.7 and §3.4 of my online notes, as well as a new §3.9, which attempt to address several questions of interpretation that I have been asked recently.

4/22/11

We have tentatively agreed that there will be no midterm, and that there will be a takehome final.

Grades will therefore be based 50% on homework and 50% on the final.
If that's not what you want, let me know as soon as possible so that we can discuss it further.

4/15/11

The figures I had intended to show today can be found here.

4/9/11

I have upated the online notes for both this class and the previous class on differnential forms.

There is new material on geodesics and symmetries in both Chapter 2 of the relativity notes and Chapter 8 of the differential forms notes.

The suggested reading for Week 2 has been updated retroactively.

4/7/11

Websites where you can determine distances on the Earth can be found here or here.

4/4/11

REMINDER: The MTH 434/534 final exam review will be tonight at 5:30 PM in Weniger 304.

The differential form review will take place Wednesday at 6 PM.

A new homework assignment has been posted, due this Friday.

4/1/11

I hope to update the online notes over the weekend...
In the meantime, a brief discussion of timelike/spacelike/lightlike lines can be found here.

3/31/11

A summary of the rules for drawing spacetime diagrams can be found here.

3/30/11

The MTH 434/534 final review session will take place next Monday (4/4) at 5:30 PM in Weniger 304.

The differential forms review session is tentatively scheduled for next Wednesday (4/6) at 6 PM.

3/28/11

The two "review" sessions are tentatively scheduled for next Monday (4/4) and Wednesday (4/6) at 5:30 PM in Weniger 304. On Monday I will go over the MTH 434/534 final, and on Wednesday I will provide an intensive summary of the use of differential forms.

Please let me know as soon as possible if you wish to attend these sessions but have a conflict with these times.

3/26/11

I will offer two optional "review" sessions, at times to be arranged. The first will go over the final from MTH 434/534, and the second is intended as an intensive summary of the use of differential forms.

Please be prepared to discuss times for these sessions on the first day of class.
Likely possibilities are Mon and/or Wed at 5:30 PM during Week 1 and/or Week 2.

(We will probably not use differential forms until Week 3.)

3/8/11

The primary text for this course will be my own course notes, which will be written as we go along. You may also wish to purchase a more traditional text, in which case I recommend one of the first three optional texts, described in more detail below. The level of this course will be somewhere between that of these texts, henceforth referred to as EBH (Taylor & Wheeler), Relativity (d'Inverno), and Gravity (Hartle).

• EBH uses only basic calculus to manipulate line elements, and only discusses black holes, but does so in great detail.
• Relativity discusses the math first, then the physics.
• 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. This book is the most advanced of the three, and is aimed at advanced undergraduate physics majors.

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

• 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 Relativity easier to read. It covers more topics more quickly than Gravity.
• 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 most of the tensor analysis in Gravity or Relativity.

In short, none of these books is perfect, but all are valuable resources. In addition to the above books, OSU owns an electronic copy of Relativity Demystified, which summarizes many of the key aspects of relativity, but provides no derivations. By all means use it for reference, but I would not recommend using it as a primary text.