3+1 Formalism and Bases of Numerical Relativity

2007/03/06 by Eric Gourgoulhon, Gourgoulhon, Eric · 1 voice · 25 citations
Mathematics · Physics and Astronomy · #Astrophysics (astro-ph) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #astro-ph #gr-qc #math.DG

paper · pdf · doi:10.48550/arxiv.gr-qc/0703035

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

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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Discussions

• Out of order, but this one is a misconception that influences other aspects of the question: In short: how do we consistently set up the initial data for something as conceptually simple as “three poi [stackexchange, 3 points]

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