Physics 387N - Spring 1998

Physics 387N: Relativity Theory II (Spring 1998)

Schedule: Tue, Thu 12:30 - 2:00 PM --- RLM 5.116 --- Unique # 54055

Instructor: M.W. Choptuik
Office: RLM 9.208A --- Office Hours: Mon, Wed 10:00-11:30 and by appointment
Phone: 471-1541 --- E-mail: matt@infeld.ph.utexas.edu
Instructor's Home Page: http://wwwrel.ph.utexas.edu/Members/matt/welcome.html
Course Home Page: http://wwwrel.ph.utexas.edu/Members/matt/Teaching/98Spring/Phy387N/Syllabus.html

Syllabus

News (last updated, Monday, Apr. 21, 3:30pm)

Course Notes

Course-Related Software

Group Pages

Project Handouts

PHY381C (Comp. Physics) Home Page including links to Notes, Software & Homework

Recommended Text: General Relativity by R. M. Wald, The University of Chicago Press, 1984.

Course Overview: This course will focus on providing students with an understanding of the formalisms and computational approaches which are currently of most use in studying strong-field aspects of classical general relativity. Lecture topics will include

The Lagrangian formulation of general relativity and other classical field theories (3)
The 3+1 (ADM/Hamiltonian) formulation of GR (3)
The initial-value problem for GR (2)
The evolution problem & coordinate (``gauge'') choices (3)
Spherically symmetric collapse, black hole formation and critical phenomena (7)
Black hole excision (3)
Adaptive mesh refinement techniques(3)
Class presentations (2)

(numbers in parentheses indicate roughly how many lectures will be devoted to each topic). Class work will consist primarily of three assigned projects and a term project, all of which will be performed in the context of 3-person teams, whose composition will be determined by the instructor. This work will have a significant computational component, and although computational techniques will be discussed in class from time to time, you may have to ``osmose'' certain skills from the instructor or other members of your team during non-class hours. Computational topics which will be encountered in the course include:

Unix
Fortran 77
Solving ODEs using canned software.
Solving linear systems using canned software.
Solving non-linear equations using Newton's method.
Solving time-dependent PDEs using finite-difference approximations (FDAs)
Solving elliptic PDEs using FDAs and multi-grid techniques
Scientific visualization using homegrown (such as ser) and commercial (such as Explorer) software.

As with all of the instructor's current computationally-oriented courses, the preferred course language is Fortran 77. Teams are not prohibited from using other languages, but the instructor will not necessarily provide the same level of support for those languages as for Fortran 77. Please follow the hyperlinks for some basic on-line material on the above topics.

Other References: As the course proceeds, a number of additional references will be used, and will be noted here.

Grades: Projects and Exam:

Course grades will be determined on the basis of performance on three assigned group projects, one term group project, and an open-book final exam, with the following weighting:

Assigned projects: 50%
Term projects: 40% (35% write-up, 5% oral presentation)
Final Examination (open book): 10% (Friday, May 15, 2:00-5:00 pm)

As mentioned above, teams will consist of three (possibly four) students and will be chosen by the instructor. Note: Due to the nature of this course, the effort required for a CR (credit) is unlikely to be significantly different than the effort required for a good grade---students who have registered CR/NOCR for this course will probably want to take this into account.

Assigned projects

Assigned projects should be treated much like regular homework assignments except that team members must work together to complete the projects. For the most part, the instructor will leave it to the individual teams to ensure that a reasonable balance of work is achieved within each team. Unlike previous courses you may have taken from the instructor, late projects are unlikely to be accepted without an extremely good excuse.

Term projects

On or before Thurs., March 12, 1998 (the last class day before spring break), each team must present the instructor with a one page summary of their term project, whose topic must have previously been cleared with the instructor. The instructor will be happy to suggest term-project topics, but also encourages the teams to pursue, if possible, specific computations of mutual interest. Term-project write-ups will be graded on the basis of a written report (estimated length 20-30 pages including figures and other results), and on an in-class oral presentation (roughly 30 minutes). The written report must be prepared in LaTeX (or TeX) and must be submitted to the instructor on or before the last class day, Thurs., May 7, 1998 (no exceptions!) The oral presentation per se may be given by any number of group members, although all members should contribute to the preparation of the presentation. Presentation order will be chosen randomly.

Final exam

The final exam consists of the single question: Write a short (1000-1500 word) essay on a subject in general relativity of your own choosing. All topics must be cleared before the time of the final, which is tentatively Friday, May 15, 2:00-5:00 pm. Essays may be completed in the official exam period or at any previous time, but completed essays must be personally handed to the instructor during the official exam (i.e. you must officially show up for the exam). Again, if need be, the instructor will assist you in choosing a topic. Note that a particularly good time to complete the essay is early in the term before the other course work starts piling up! Essays need not be typed or word-processed, but must be legible.

Computer Access:

All students should have an account on the Physics Dept. public Unix systems located in the Graduate Computer Lab, RLM 3.118. More importantly, you will be given access to the Center for Relativity Unix machines. and will be expected to use these machines extensively for your group work. Note that most of these machines are in grad student and post-doc offices so you should not expect to be able to use any given machine on demand. However, I do not anticipate access to machines being particularly problematic in the context of completion of group work: if you do encounter such difficulties, contact the instructor immediately. Teams will also be provided with access to high-performance machines operated by the Texas Advanced Computing Center .

Miscellaneous Administrative Notes:

Please note the following cut-off dates. See the UT Austin Spring 1998 Course Schedule for more information.

Feb 16, 1998: Last day to drop a course without a possible academic penalty.
May 8, 1998: Last day a graduate student may, with the approval of the instructor, the graduate adviser, and the graduate dean, drop a course.

Syllabus

Due Tuesday Thursday

January 20
Introduction (GR15 talk) January 22
Lagrangian GR

January 27
Lagrangian GR January 29
Lagrangian GR

February 3
3+1 GR February 5
3+1 GR
Project 1
(2/12) February 10
3+1 GR February 12
3+1 GR

February 17
3+1 GR February 19
3+1 GR

February 24
Initial Value Problem February 26
Evolution & Coordinates
Project 2
(3/5) March 3
Spherical symmetry March 5
Spherical symmetry
Term Project
Outlines (3/12) March 10
Collapse & BH formation March 12
Collapse & BH formation

March 17
Spring Break March 19
Spring Break

March 24
Critical Phenomena March 26
Critical Phenomena

March 31
Critical Phenomena April 2
Critical Phenomena
Project 3
(4/9) April 7
BH excision April 9
BH excision

April 14
BH excision April 16
BH excision

April 21
AMR April 23
AMR

April 28
AMR April 30
Group presentations
Term Projects
(5/7) May 5
Group presentations May 7
Presentations & Class Evaluation

Due	Tuesday	Thursday
	January 20 Introduction (GR15 talk)	January 22 Lagrangian GR
	January 27 Lagrangian GR	January 29 Lagrangian GR
	February 3 3+1 GR	February 5 3+1 GR
Project 1 (2/12)	February 10 3+1 GR	February 12 3+1 GR
	February 17 3+1 GR	February 19 3+1 GR
	February 24 Initial Value Problem	February 26 Evolution & Coordinates
Project 2 (3/5)	March 3 Spherical symmetry	March 5 Spherical symmetry
Term Project Outlines (3/12)	March 10 Collapse & BH formation	March 12 Collapse & BH formation
	March 17 Spring Break	March 19 Spring Break
	March 24 Critical Phenomena	March 26 Critical Phenomena
	March 31 Critical Phenomena	April 2 Critical Phenomena
Project 3 (4/9)	April 7 BH excision	April 9 BH excision
	April 14 BH excision	April 16 BH excision
	April 21 AMR	April 23 AMR
	April 28 AMR	April 30 Group presentations
Term Projects (5/7)	May 5 Group presentations	May 7 Presentations & Class Evaluation