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3+1 Formalism and Bases of Numerical Relativity

Eric Gourgoulhon
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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.

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Eric Gourgoulhon. 2007-03-06. 3+1 Formalism and Bases of Numerical Relativity. https://arxiv.org/abs/gr-qc/0703035

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