Trumpet slices of the Schwarzschild-Tangherlini spacetime

TL;DR

This paper investigates trumpet-shaped spatial slices in higher-dimensional Schwarzschild-Tangherlini black holes, generalizing known slicing conditions and demonstrating numerical evolution to these geometries in five dimensions.

Contribution

It extends the analysis of trumpet slices to D-dimensional black holes and develops a numerical code for evolving these slices in 5D.

Findings

Identified special trumpet slices in D-dimensional Schwarzschild-Tangherlini spacetime.

Generalized 1+log slicing condition parametrized by n.

Numerical simulations in 5D settle to trumpet solutions.

Abstract

We study families of time-independent maximal and 1+log foliations of the Schwarzschild-Tangherlini spacetime, the spherically-symmetric vacuum black hole solution in D spacetime dimensions, for D >= 4. We identify special members of these families for which the spatial slices display a trumpet geometry. Using a generalization of the 1+log slicing condition that is parametrized by a constant n we recover the results of Nakao, Abe, Yoshino and Shibata in the limit of maximal slicing. We also construct a numerical code that evolves the BSSN equations for D=5 in spherical symmetry using moving-puncture coordinates, and demonstrate that these simulations settle down to the trumpet solutions.