3+1 Formalism and Bases of Numerical Relativity
By E. Gourgoulhon. 2007
384 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Theoretical Computer Science
View Paper: https://www.semanticscholar.org/paper/a408a8804e15199019fc2bf64e56c94ae0cbad5e
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In Geometry and Topology
In Theoretical Computer Science
Citations in the corpus
- Dynamical boson stars (2012, neutral): “It is therefore more intuitive to instead consider a succession of spacetime geometries, where the evolution of a given slice is given by the Einstein equations (for more detailed treatments see [9, 34, 50, 167]).”
- Black-hole binaries, gravitational waves, and numerical relativity (2010, background): “For more detailed treatments, we direct the interested reader to Alcubierre (2008) or (Gourgoulhon, 2007).”
- Effective field theory of dark energy: A review (2019, methodology): “Now we use the Gauss-Codazzi relation [109] to write the above action in the ADM formalism:”