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arxiv: 1603.00362 · v1 · pith:X65IXUEMnew · submitted 2016-03-01 · 🌀 gr-qc · hep-th

Dimensional reduction in numerical relativity: Modified cartoon formalism and regularization

William G. Cook , Pau Figueras , Markus Kunesch , Ulrich Sperhake , Saran Tunyasuvunakool This is my paper
classification 🌀 gr-qc hep-th
keywords casemethoddimensionaldimensionsnumericalsymmetryaxisymmetrybaumgarte-shapiro-shibata-nakamura
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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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