  We report on the end state of nonaxisymmetric instabilities of singly
spinning asymptotically flat Myers-Perry black holes. Starting from a singly
spinning black hole in D=5,6,7 dimensions, we introduce perturbations with
angular dependence described by m=2, m=3, or m=4 azimuthal mode numbers about
the axis of rotation. In D=5, we find that all singly spinning Myers-Perry
black holes are stable, in agreement with the results from perturbation theory.
In D=6 and 7, we find that these black holes are nonlinearly stable only for
sufficiently low spins. For intermediate spins, although the m=2 bar mode
becomes unstable and leads to large deformations, the black hole settles back
down to another member of the Myers-Perry family via gravitational wave
emission; surprisingly, we find that all such unstable black holes settle to
the same member of the Myers-Perry family. The amount of energy radiated into
gravitational waves can be very large, in some cases more than 30% of the
initial total mass of the system. For high enough spins, the m=4 mode becomes
the dominant unstable mode, leading to deformed black holes that develop local
Gregory-Laflamme instabilities, thus forming a naked singularity in finite
time, which is further evidence for the violation of the weak cosmic censorship
conjecture in asymptotically flat higher-dimensional spacetimes.
