Dimensional reduction in numerical relativity: Modified Cartoon formalism and regularization
William G. Cook, Pau Figueras, Markus Kunesch, Ulrich Sperhake, Saran Tunyasuvunakool
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Source: Crossref
Published: Aug 1, 2016
DOI: 10.1142/s0218271816410133
Open original source ↗Source abstract
We present in detail the Einstein equations in the Baumgarte–Shapiro–Shibata–Nakamura formulation for the case of [Formula: see text]-dimensional spacetimes with [Formula: see text] isometry based on a method originally introduced in Ref. 1. Regularized expressions are given for a numerical implementation of this method on a vertex centered grid including the origin of the quasi-radial coordinate that covers the extra dimensions with rotational symmetry. Axisymmetry, corresponding to the value [Formula: see text], represents a special case with fewer constraints on the vanishing of tensor components and is conveniently implemented in a variation of the general method. The robustness of the scheme is demonstrated for the case of a black-hole head-on collision in [Formula: see text] spacetime dimensions with [Formula: see text] symmetry.
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