# End point of nonaxisymmetric black hole instabilities in higher dimensions

## TL;DR

This study investigates the nonlinear stability and end states of higher-dimensional rotating black holes, revealing stability in five dimensions and complex instability behaviors in six and seven dimensions, including potential violations of cosmic censorship.

## Contribution

It provides the first nonlinear analysis of nonaxisymmetric instabilities in higher-dimensional black holes, showing how these black holes evolve and settle or develop singularities depending on their spin.

## Key findings

- All five-dimensional singly spinning Myers-Perry black holes are stable.
- In six and seven dimensions, black holes are stable only at low spins.
- High-spin black holes develop instabilities leading to potential naked singularities.

## Abstract

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.