3+1 Formalism in General Relativity: Bases of Numerical Relativity
Eric Gourgoulhon
Springer, 2012
294 pages
Contents:
1. Introduction
2. Basic Differential Geometry
3. Geometry of Hypersurfaces
4. Geometry of Foliations
5. 3+1 Decomposition of Einstein Equation
6. 3+1 Equations for Matter and Electromagnetic Field
7. Conformal Decomposition
8. Asymptotic Flatness and Global Quantities
9. The Initial Data Problem
10. Choice of Foliation and Spatial Coordinates
11. Evolution Schemes
A. Conformal Killing Operator and Conformal Vector Laplacian
B. Sage Codes
More details at http://relativite.obspm.fr/3p1