Accepted Tuesday Oct 27, 2009
It has been conjectured that higher-dimensional rotating black holes become unstable at a sufficiently large value of the rotation, and that new black holes with pinched horizons appear at the threshold of the instability. We search numerically, and find, the stationary axisymmetric perturbations of Myers-Perry black holes with a single spin that mark the onset of the instability and the appearance of the new black hole phases. The instability sets in, to a few per-mil precision, at the rotation for which the second derivative of the entropy with respect to angular momentum vanishes. We conjecture that this can be extended to predict ultraspinning instabilities in more generality. We also find new ultraspinning Gregory-Laflamme instabilities of rotating black strings and branes.