Trumpet slices of the Schwarzschild-Tangherlini spacetime

Abstract

We study families of time-independent maximal and $1+\mathrm{log}$ foliations of the Schwarzschild-Tangherlini spacetime, the spherically symmetric vacuum black hole solution in $D$ spacetime dimensions, for $D\ensuremath{\ge}4$. We identify special members of these families for which the spatial slices display a trumpet geometry. Using a generalization of the $1+\mathrm{log}$ slicing condition that is parameterized 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 Baumgarte-Shapiro-Shibata-Nakamura equations for $D=5$ in spherical symmetry using moving-puncture coordinates and demonstrate that these simulations settle down to the trumpet solutions.