Minicourse on Numerical Relativity

Start time: March 28, 2016

Ends on: April 1, 2016


  • Luis Lehner (Perimeter Institute -Waterloo, Canada)
  • Vasileios Paschalidis (Princeton University, USA)
  • Frans Pretorius (Princeton University, USA)

Title: A first course on Numerical Relativity

Location: São Paulo, Brazil



This course will cover the fundamentals of solving Einstein equations numerically in strongly gravitating/dynamical regimes. Emphasis will be on fundamentals to lay a solid foundation for venturing into Numerical Relativity. Topics to be covered include: Numerical Analysis for Partial Differential Equations, Formulations of Einstein equations, Hydrodynamics and basics of applications for Astrophysics, fundamental questions on General Relativity and Holography. While no formal training on coding will be assumed, it would be helpful if participants have a basic knoweldge of Maple, Mathematica, Matlab, Fortran, C or Python to carry out related exercises. Financial support will be available for graduate students and researchers from South America that would like to attend the minicourse. 




List of Confirmed Participants: Updated on March 23

Satisfaction Survey:


School Program: PDF updated on March 29

 Click on the title of the lectures to watch the videos and on (PDF) to download the lecture files.

Start End Monday, March 28 Tuesday, March 29 Wednesday, March 30 Thursday, March 31 Friday, April 1
8:30 9:30 Registration
9:30 11:00 Introduction
L. Lehner

FD, basics, boundaries, hyperbolicity  (Vídeo 2)
V. Paschalidis (PDF)

Decomposition of Einstein, ADM
F. Pretorius
Hydro equations
L. Lehner
Ideal MHD (PDF)
V. Paschalidis
Adaptive mesh refinement
F. Pretorius
11:30 13:00 Basics; Ex: Minkwoski wave eqn.
L. Lehner
BSSN/GH formulations and contraint damping
F. Pretorius
Num. methods for hydro, HRSC (PDF)
V. Paschalidis
Force-free equations & methods
L. Lehner
Characteristic formulations and applications
L. Lehner
14:30 19:00 Pre-discussion: tools, visualization, and related.

Lab: 1D wave eqn,  Maxwell (optional)

Turbulence and fluid/gravity correspondence in AdS/CFT
L. Lehner

Lab: Wave eqn on a BH background, spherical symmetry. Dynamical background (optional)

IFT-Colloquium: The Dynamical Strong-field Regime of General Relativity (PDF)
F. Pretorius (at 2 pm)

Lab: Burgers eqn (FD, HRSC)

Discussion: The Dynamical Strong-field Regime of General Relativity
F. Pretorius

Lab: Relativistic hydro, FF (optional)

Discussion: gauges + others
V. Paschalidis

Lab: wrap up of projects

Discussion: Round table of future problems & opportunities

Additional Notes:

Notes on constraint damping for Maxwell´s equations; L. Lehner, V. Paschalidis, F. Pretorius

Frans Pretorius Lectures

Lab sessions:



Simple Wave

Wave on bh

Simple fluid 2D

Spherically symmetric back-reacting code:

Lectures – Reading Material:

It is highly recommended that potencial participants read the references below before the starting of the minicourse:

1. Relativistic Astrophysics and Numerical Relativity Numerical Analysis for Numerical Relativists; Matthew W. Choptuik

2. Spacetime and Geometry: An Introduction to General Relativity; Sean M. Carrol

3. General Relativity; Robert M. Wald (Chapters 1-6)


Additional Information:

Registration: ALL participants should register. The registration will be on March 28 at the institute, from 8:30 to 9:30.  You can find arrival instruction at

Accommodation: Participants whose accommodation has been provided by the institute will stay at The Universe Flat. Each participant, whose accommodation has been provided by the institute, has received the accommodation details individually by email.

Emergency number: 9 8233 8671 (from São Paulo city); +55 11 9 8233 8671 (from abroad), 11 9 8233 8671 (from outside São Paulo).

Ground transportation instructions: 

Ground transportation from Guarulhos Airport to The Universe Flat

Ground transportation from Congonhas Airport to the Universe Flat

Ground transportation from The Universe Flat to the institute