Maximal slicing of D-dimensional spherically-symmetric vacuum spacetime

TL;DR

This paper investigates maximal hypersurface foliations in higher-dimensional spherically symmetric black-hole spacetimes, providing analytic solutions for D=5 and demonstrating their singularity-avoiding properties for numerical relativity.

Contribution

It extends the study of maximal slicing to D≥5 dimensions, offering analytic solutions for D=5 and showing the utility of these foliations in higher-dimensional numerical relativity.

Findings

Maximal hypersurfaces avoid singularities in higher dimensions.

Analytic solutions are provided for D=5 stationary maximal slices.

Foliations are useful for numerical simulations of higher-dimensional black holes.

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.