Physics 555B: Numerical Relativity (Spring 2005)

(Directed studies: 3 Credit Hours)


Please report bugs, suggestions etc. to Matt


  1. Bryan Kelleher
    Office: Hennings 330A
    Office phone: 822-5879
    Office hours: TBA

  2. Matthew (Matt) W. Choptuik
    Office: Hennings 403
    Office phone: 822-2412
    Home phone: 222-9424
    Office hours: Drop-in (appointment via e-mail phone recommended)

  3. Martin Snajdr
    Office: Hennings 408B
    Office phone: 822-3860
    Office hours: TBA
Course Home Page:


  1. Working knowledge of general relativity and associated mathematics, including tensor calculus
  2. Computational physics at the level of PHYS 410



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

(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 2-person teams, whose composition will be determined by students in consultation with 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: The preferred course language is Fortran 77. Teams are not prohibited from using other languages, but the instructors 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.


Course grades will be determined on the basis of performance on three assigned group projects and one term group project with the following weighting: As mentioned above, teams will consist of two students, with composition to be chosen by the students in consultation with the instructors.

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 instructors, late projects are unlikely to be accepted without an extremely good excuse.

Term projects

On or before 1:30 PM, February 22, each team must present the instructors with a one page summary of their term project, whose topic must have previously been cleared with Choptuik. Choptuik 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 Choptuik on or before a date that will be subsequently announced (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.


Tuesday Thursday
January 11
Lagrangian approach to GR
January 13
Lagangian approach to GR
January 18
Lagrangian approach to GR
January 20
The 3+1 formulation of GR
January 25
The 3+1 formulation of GR
January 27
The 3+1 formulation of GR
February 1
The 3+1 formulation of GR
February 3
The 3+1 formulation of GR
February 8
The initial-value problem for GR
February 10
The initial-value problem for GR
February 15
February 17
February 22
The evolution problem & coordinate choices
February 24
The evolution problem & coordinate choices
March 1
Spherical symmetry
March 3
Spherical symmetry
March 8
Spherical symmetry
March 10
Spherical symmetry / General relativistic hydrodynamics
March 15
General relativistic hydrodynamics
March 17
General relativistic hydrodynamics
March 22
General relativistic hydrodynamics
March 24
General relativistic hydrodynamics
March 29
General relativistic hydrodynamics
March 31
Selected topics incl. BH critical phen.
April 5
Selected topics incl. BH critical phen.
April 7
Selected topics incl. BH critical phen.
Group presentations

Syllabus Notes

Other Important Dates

See the UBC 2004/2005 Calendar, Academic Year, PHYS Exam Schedule, Exam Schedule pages for more information