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arXiv · 1603.00362

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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Abstract

We present in detail the Einstein equations in the Baumgarte-Shapiro-Shibata-Nakamura formulation for the case of $D$ dimensional spacetimes with $SO(D-d)$ 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 $d=D-2$, 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 $D=7$ spacetime dimensions with $SO(4)$ symmetry.

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William G. Cook, Pau Figueras, Markus Kunesch, Ulrich Sperhake, Saran Tunyasuvunakool. 2016-03-01. Dimensional reduction in numerical relativity: Modified cartoon formalism and regularization. https://doi.org/10.1142/s0218271816410133

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