Syllabus: Numerical Relativity (PHZ 7609) - Spring 2025

Class times and location: Tuesday and Thursday 14:00 - 15:20, SE 319

Instructor: Wolfgang Tichy
Office: Science and Engineering (SE) 444
E-mail: wolf "at" fau.edu (be sure to put PHY 6938 in the subject line)
Phone: 7-3380
Class Website: http://www.physics.fau.edu/~wolf/Teaching/2025_NumRel

Office Hours: Tuesdays 15:20-16:20, Thursdays 15:20-16:20, and by appointment

Textbooks:
M. Alcubierre, Introduction to 3+1 Numerical Relativity (Oxford Science Publications)
A. P. Lightman, W. H. Press, R. H. Price and S. A. Teukolsky, problem book in relativity and gravitation (Princeton University Press, 1975)

Other books worth looking at:
Eric Gourgoulhon, 3+1 Formalism and Bases of Numerical Relativity ( https://arxiv.org/abs/gr-qc/0703035 )
S. M. Carroll, An Introduction to General Relativity Spacetime and Geometry (Pearson/Addison Wesley, 2004)
C. Misner, K. Thorne and J. Wheeler, Gravitation (Freeman, 1973)
R. Wald, General Relativity (Chicago, 1984)
S. Weinberg, Gravitation and Cosmology (Wiley, 1972)
P. A. M. Dirac, General Theory of Relativity (Wiley, 1975)

Course objectives:
The course will give an overview of Numerical Relativity. It is intended to be a second graduate course in General Relativity. The course is self contained, but some prior knowledge of General Relativity is expected. In the beginning we review a number of mathematical tools used in General Relativity. These tools will then be used to derive the 3+1 formulation of General Relativity. Within this formulation we then discuss how compact objects such as black holes or neutron stars can be evolved and simulated on computers. The lectures will set the pace for the course, but problem solving is an essential part of this course. The students are expected to study on their own by reading assigned texts and by solving assigned problems.

Topics covered:

  1. Review of General Relativity:
    spacetime, metric, vectors, one-forms, curves, tensors, Lie derivatives, coordinate transformations, covariant derivatives, curvature, Einstein Equations, stress-energy tensor
  2. 3+1 formalism:
    3+1 split, extrinsic curvature, ADM evolution and constraint equations, BSSNOK equations
  3. Initial data:
    conformal transverse traceless decomposition, conformal thin-sandwich decomposition, quasi-circular orbits, examples of initial data
  4. Gauge conditions:
    slicing conditions, shift conditions
  5. Hyperbolicity and evolution of vacuum spacetimes:
    introduction to well-posedness, discussion of BSSNOK, boundary conditions
  6. Relativistic Hydrodynamics:
    GR hydrodynamics, 3+1 form of the hydro equations, equations of state, hyperbolicity and flux conservative schemes
  7. Numerical methods:
    concepts of finite differencing, stability analysis, boundary conditions, convergence testing

Homework: All homework problems will be posted on the class website. The first few problem sets will not be graded. The due dates for the graded problem sets will be posted on the class website. You will loose about 10% of the maximum score for each day your homework is late. Please note that it is essential that you do all problem sets (graded or not). This is the only way for you to learn.
Homework policy: You must solve the problems yourself. This is the optimal way to learn the material. If you are stuck on a problem you may discuss it with other students or the instructor. However, this discussion should be limited to understanding the essential point(s) so that you can go ahead and solve most of the problem yourself. In particular, do not use solution sets from problem/solution books, or any other sources to simply look up your homework problems!

Grades will be based on the following:
Activity Percentage
Homework 25%
Class Participation 5%
Midterm Exam 30%
Final Exam 40%

Tentative exam dates:
Midterm Exam: 3/18/2025 in class
Final Exam: 4/29/2025 from 10:00 - 12:30 in SE 319

Exam Make up policy:
In general any missed exam will count as if the student has obtained zero points. If the student can convince the instructor that the exam was missed for a good reason, the student's grade will be computed from the remaining exams and homework.


Strange Florida law issues:

Students enrolled in this course may be allowed to record video or audio of class lectures in certain cases. To find out more read, the official university policies.
But even in allowed cases, it is much more polite (and also prudent) to ask for instructor agreement before starting to record.


FAU policy statements:
Please see the so called "Simple Syllabus" in Canvas for all official FAU policies.