Maximal slicing of D-dimensional spherically-symmetric vacuum spacetime

Abstract

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.

20 pages, 8 figures

References in corpus (8)

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• Binary black-hole evolutions of excision and puncture data
• The high-energy collision of two black holes
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Cited by in corpus (8)

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• Semianalytical estimates of scattering thresholds and gravitational radiation in ultrarelativistic black hole encounters
• Ultra-relativistic grazing collisions of black holes
• Numerical relativity for D dimensional axially symmetric space-times: formalism and code tests
• Black holes in a box: towards the numerical evolution of black holes in AdS
• Trumpet slices of the Schwarzschild-Tangherlini spacetime
• Floating Black Hole in the Karch-Randall Model and its Holographic Dual
• Constant-mean-curvature Slicing of the Swiss-cheese Universe