Maximal slicing of D-dimensional spherically-symmetric vacuum spacetime

Details Maximal slicing of D-dimensional spherically-symmetric vacuum spacetime Maximal slicing of D-dimensional spherically-symmetric vacuum spacetime

2009-08-06

arxiv.org/abs/0908.0799v1

Phys.Rev.D80:084028,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, 8 figures

Scientific paper

10.1103/PhysRevD.80.084028

We study the foliation of a $D$-dimensional spherically symmetric black-hole spacetime with $D\ge 5$ by two kinds of one-parameter family of maximal hypersurfaces: a reflection-symmetric foliation with respect to the wormhole slot and a stationary foliation that has an infinitely long trumpet-like shape. As in the four-dimensional case, the foliations by the maximal hypersurfaces have the singularity avoidance nature irrespective of dimensionality. This indicates that the maximal slicing condition will be useful for simulating higher-dimensional black-hole spacetimes in numerical relativity. For the case of D=5, we present analytic solutions of the intrinsic metric, the extrinsic curvature, the lapse function, and the shift vector for the foliation by the stationary maximal hypersurfaces. This data will be useful for checking five-dimensional numerical relativity codes based on the moving puncture approach.

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