Eric GOURGOULHON (LUTH, CNRS / Observatoire de Paris)

3+1 Formalism and Numerical Relativity

6 lectures: 19, 23, 24, 25, 26, 27 October 2006

Lecture notes (also available as arxiv.org/abs/gr-qc/0703035)


Lecture 1 : Thursday 19 October, 10 am - 1 pm :

1. Geometry of hypersurfaces

2. Geometry of foliations


Lecture 2 : Monday 23 October, 10 am - 1 pm :

3. 3+1 decomposition of Einstein equation

4. 3+1 form of the matter equations


Lecture 3 : Tuesday 24 October, 10 am - 1 pm :

5. Global quantities

6. Conformal decomposition


Lecture 4 : Wednesday 25 October, 10 am - 1 pm :

7. Initial data problem


Lecture 5 : Thursday 26 October, 10 am - 1 pm :

8. Choice of coordinates

9. Treatment of black holes


Lecture 6 : Friday 27 October, 10 am - 1 pm :

10. Numerical techniques to solve the 3+1 equations

11. Review of numerical results