3+1 Formalism and Bases of Numerical Relativity

Details 3+1 Formalism and Bases of Numerical Relativity 3+1 Formalism and Bases of Numerical Relativity

2007-03-06

arxiv.org/abs/gr-qc/0703035v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Lectures given at the General Relativity Trimester held in the Institut Henri Poincare (Paris, Sept.-Dec. 2006) and at the VII

Scientific paper

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.

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