  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. We also find new
ultraspinning Gregory-Laflamme instabilities of rotating black strings and
branes.
