Titlebook: 3+1 Formalism in General Relativity; Bases of Numerical R Eric Gourgoulhon Book 2012 Springer-Verlag Berlin Heidelberg 2012 3+1 formalism a

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David S. Wishart,Marcia A. Levatter deriving the general laws of energy conservation and momentum conservation from the vanishing of the divergence of the stress-energy tensor, we focus on the particular case of a perfect fluid. We introduce the basic quantities describing the fluid from the point of view of the Eulerian observer an

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A Practical Guide to Ore Microscopy—Volume 1e 3 + 1 foliation: the ADM mass, the ADM linear momentum, the total angular momentum, the Komar mass and the Komar angular momentum. For each of these quantities, we derive expressions in terms of the 3+1 objects and provide some concrete examples.

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A Practical Guide to Ore Microscopy—Volume 1nformal decomposition introduced in Chap. 7: the conformal transverse-traceless method and the conformal thin sandwich method. Both methods are illustrated by initial data in Schwarzschild spacetime. Finally, we give a survey of the construction of initial for binary compact objects, which are of ma

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https://doi.org/10.1007/978-3-031-12654-3function: the geodesic, maximal, harmonic, and 1+log slicings are presented here. In a second stage, we focus on of the propagation of the spatial coordinates from slice to slice, via the choice of the shift vector. We introduce the concepts of normal coordinates, minimal distortion and variants of

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978-3-642-24524-4Springer-Verlag Berlin Heidelberg 2012

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https://doi.org/10.1007/978-3-031-12654-3Various approaches to evolve forward in time the 3+1 Einstein equations are discussed. After a review of constrained schemes, we focus on free evolution schemes, giving some details about the propagation of the constraints. Among the free evolution schemes, a particular important one is the BSSN scheme, which is presented here in details.

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