The End Point of Nonaxisymmetric Black Hole Instabilities in Higher Dimensions

We report on the end state of non-axisymmetric 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 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 non-linearly 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 80% 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.