3+1 Formalism and Bases of Numerical Relativity

Abstract

These lecture notes provide some introduction to the 3+1 formalism of general relativity, which is the foundation of most modern numerical relativity. The text is rather self-contained, with detailed calculations and numerous examples. Contents: 1. Introduction, 2. Geometry of hypersurfaces, 3. Geometry of foliations, 4. 3+1 decomposition of Einstein equation, 5. 3+1 equations for matter and electromagnetic field, 6. Conformal decomposition, 7. Asymptotic flatness and global quantities, 8. The initial data problem, 9. Choice of foliation and spatial coordinates, 10. Evolution schemes.

Lectures given at the General Relativity Trimester held in the Institut Henri Poincare (Paris, Sept.-Dec. 2006) and at the VII Mexican School on Gravitation and Mathematical Physics (Playa del Carmen, Mexico, 26. Nov. - 2 Dec. 2006), 220 pages, 25 figures. Corrections and suggestions are welcome

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