Trumpet slices of the Schwarzschild-Tangherlini spacetime

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.