End point of nonaxisymmetric black hole instabilities in higher dimensions

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 what appear to be 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.