ANNOUNCEMENTS
MTH 437/537 — Spring 2013

6/18/13

Grades should now be posted.

The average score on the final was 61 out of 80; the median score was 69.

I should be in my office on Wednesday, 6/19, from roughly 10–12 and 1–3 (the latter time is for exam pickup only).

6/13/13

I am roughly halfway done grading the final exams, and hope to finish tomorrow (Friday). Course grades are therefore unlikely to be available before Monday.

• You can collect your exam from me, and look at worked solutions, in my office, but you'll have to find me there; my schedule varies considerably during the summer. Feel free to contact me via email to inquire about possible times.
• I have posted some comments on the exam questions here.

6/9/13

Kidder is locked! If you can't get in:

• Call my office: (541) 737-5159.
• Go to the north entrance, which is directly below my office, and shout.

6/8/13

Exam Clarification:

• The "last problem" referred to in problem 2 is Problem 4 (the last problem on the exam), not Problem 1 (the previous problem)...
• Also in problem 2, "orbit" in this context implies "geodesic".
• In problem 3, "its lifetime" refers to the lifetime of the universe.
• Also in problem 3, b and c are constants (and c is not the speed of light).

6/7/13

Further information about the Alcubierre "warp drive" geometry can be found on Wikipedia.

The original paper can be found here.

Corrected Penrose diagrams for some of the Dray-'t Hooft geometries can be found here.

The recent paper on which they are based can be found here.

6/6/13

I plan to hold extensive office hours during the take-home final:

• Friday, 6/7, from 1–3:30 PM. (Later times may be possible by appointment.)
• Monday, 6/10, from 9–11:30 AM and from 1–3:30 PM. (Later times may be possible by appointment.)
• Tuesday, 6/11, from 9 AM until noon.

I also expect to be in my office at least one afternoon over the weekend, with the exact timing TBA
from roughly 1–2:30 PM on Saturday, 6/8, and roughly 1–3:30 PM on Sunday, 6/9.

6/5/13

Here are the figures shown in class this morning:

The Penrose diagrams for the Reissner-Nordström black hole can be found here.

The drawings of the Kerr geometry can be found here.

Both sets of figures are taken from d'Inverno's book.

6/2/13

We will have a takehome final, which is scheduled to be given out in class on Friday, 6/7, and will be due in my office at noon on Tuesday, 6/11.

The exam will be open book; you may consult any sources you wish except discussing the exam with anyone other than me. Extensive office hours will be available.

5/31/13

The table shown in class this morning, showing the classification of Friedmann solutions, can be found here. It is taken from d'Inverno's book.

5/21/13

The Robertson-Walker curvature 2-forms and Einstein tensor can be found in §8.4 of the text.

The homework asks you to justify these expressions; show your work!

Further details of the analogous computation in the Schwarzschild spacetime are now available in §A.1 of the text.

The Robertson-Walker computation at the end of the appendix will be updated next week.

5/20/13

The tentative plan for the final exam is to have a take-home exam, handed out in class on the last day (Friday, 6/7), and due at noon on the following Tuesday (6/11).

If this timing is difficult for you, please contact me as soon as possible. If more than a few people require alternate arrangements, we will likely revert to a traditional final – which would be at the assigned time of Monday at noon.

5/18/13

There will be no class on Friday, 5/24/13.

I will accept HW #6 without penalty until the due date for HW #7 (5/29). However, only if HW #6 is submitted by the original due date (5/20) will it be returned to you in time for necessary corrections to be made on HW #7.

5/17/13

I misstated the implications of the first Bianchi identity for the components of the Riemann tensor.

The correct statement now appears as Equation (4) of §7.7 of the differential forms textbook.

5/15/13

I have (hopefully) simplified the notation in Chapter 7 of the text, by minimizing the use of u•dr to denote 1-forms.

5/11/13

If you wish to use GRTensor with the JAVA-based frontend (the default), the help pages are available here.

As mentioned in class, Mathematica programs to accompany Hartle's textbook are available online.

5/10/13

Printouts of sample computer algebra sessions are available for GRTensor and CLASSI.

An older version of my instructions, that also includes coordinate-based computations, can be found here and here.

Rough instructions on using the newer DifferentialGeometry package, available in recent versions of Maple to compute curvature tensors can be found here

5/8/13

The last expression I wrote down in class this morning for ü was incorrect.

The correct expression can be found in Equation (7) of §6.3 of the text (and is derived in §6.4).

5/1/13

The figure drawn in class this morning, showing the relationship between rain coordinates and infinitesimal distance, can be found here.

The relative speed v between freely-falling observers and shell observers is given by v² = 2m/r.
As shown geometrically in the figure, ds² = − dT² + (dr + v dT)²

4/30/13

I have added a new section on null orbits to my online book.

4/29/13

My office hour on Wednesday, 5/1/13, is canceled moved to 10–10:50 AM due to an unavoidable conflict.

I will be available immediately after class.

4/19/13

The potential diagrams for orbits from today's class can be found here, along with a detailed description.

Contrary to what I implied in class, the parameter used to distinguish the curves is the angular momentum.

4/16/13

I have added a new section to the online notes, summarizing yesterday's presentation about GPS.

4/8/13

I have added a new, optional section to the online notes, describing tensors, including symmetric, rank 2 tensors such as those in Killing's equation.

Feedback is welcome; this section should be regarded a rough draft.

4/8/13

An online distance calculator using Google maps can be found here.

You can enter latitude and longitude directly in the form "45.0N 125.0W".

4/6/13

We will meet Wednesday 4/10 at 4 PM in StAg 106 to go over the MTH 434/534 final from last term.

We will end promptly at 4:50. (I have another class meeting at 5.)

4/5/13

Sample problems have been added to the review page on differential forms.

UPDATE: A formula sheet has also been added.

4/4/13

My notes from yesterday's review session, along with a list of other resources to review differential forms, are available here.

4/3/13

We will meet today at 5 PM in Weniger 304 to review differential forms.

We may need to start in Weniger 212 due to a scheduled activity in Weniger 304 that may run until 5:20.

We will meet again at a time to be arranged (not next Wednesday) to go over the MTH 434/534 final.

4/2/13

My office hours this Friday are moved to 10:15–10:45 AM. (I will be teaching a 9 AM class that day only.)

4/1/13

The slide I showed (or tried to) in class today, with the train schedule in the form of a spacetime diagram, can be found here. It is taken from Hartle's book.

3/31/13

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 Wednesday.
Likely possibilities are Mon and/or Wed at 4 PM or later (including evening) during Week 1 and/or Week 2.

(We will probably not use differential forms before the end of Week 2.)

3/22/13

We will also refer briefly to my book on special relativity. You may purchase this book if you wish, but the prepublication copy available online should be sufficient.

3/8/13

The primary text for this course will be my own course notes, which will be updated 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.