Perimeter Scholars International
Explorations in Gravitational Physics

Numerical Relativity

MW Choptuik, L Lehner & F Pretorius

Please report all errors/typos. etc to Matt Choptuik at

Last updated March 26, 2010

Quick Links: [ Project 1 : Project 2 : Project 3]

Lecture Notes

Week 1: Solution of Classical Field Equations Using Finite Difference Techniques (MW Choptuik)

  1. Solving the wave equation using finite difference techniques [PDF]
  2. The 3+1 approach to the Einstein equations [PDF]
  3. Time dependent spherically symmetric (SS) spacetimes and the SS Einstein-massless-Klein-Gordon system [PDF]
  4. Project 1 handout [PDF]

Week 2: Much Ado About Hydrodynamics and Related Problems (L Lehner)

  1. Overview and Burger's equation (includes Project 2) [PDF]
  2. General Relativistic Hydrodynamics and beyond [PDF]

Week 3: Miscellaneous topics (F Pretorius)

  1. Lecture 1: Overview [PDF]
  2. Lecture 4: AMR [PDF]

Background/Reference Material and Related Software  

Project 1: Scalar Wave Evolution on a Schwarzschild Background

Project 2: Ultrarelativistic Hydrodynamics

Project 3: Teukolsky Equation