Higher-dimensional puncture initial data

We calculate puncture initial data, corresponding to single and binary black holes with linear momenta, which solve the constraint equations of $D$-dimensional vacuum gravity. The data are generated by a modification of the pseudospectral code presented in [M. Ansorg, B. Bruegmann, and W. Tichy, Phys. Rev. D 70, 064011 (2004).] and made available as the TwoPunctures thorn inside the Cactus computational toolkit. As examples, we exhibit convergence plots, the violation of the Hamiltonian constraint as well as the initial data for $D=4,5,6,7$. These initial data are the starting point to perform high-energy collisions of black holes in $D$ dimensions.

Figure 1

Convergence plot for the $b/r_S=30.185$, $P/r_S^{D-3}=\pm 0.80$ cases.

Figure 2

$u$ function for $D=4,\dots ,7$ plotted along the $z$-axis, in units of $r_S$. We used $n_A=n_B=n=300$, $n_{\varphi }=4$. We also show a zoom around the puncture.

Figure 3

Violation of the Hamiltonian constraint along the $z$-axis, evaluated with a fourth-order finite-difference scheme. The growth of the constraint violation near the puncture is an artifact of finite-differencing across the puncture; see text for details.