Non-linear instability of slowly rotating Kerr-AdS black holes

TL;DR

This study demonstrates that slowly rotating Kerr-AdS black holes are non-linearly unstable due to persistent scalar field trapping, leading to a non-axisymmetric, time-dependent black hole state.

Contribution

First to show non-linear instability of Kerr-AdS black holes through full simulations including backreaction effects.

Findings

Stable trapping persists at the non-linear level.

Black holes evolve into non-axisymmetric, time-dependent configurations.

Kerr-AdS black holes are non-linearly unstable.

Abstract

Generic scalar perturbations on a fixed slowly rotating Kerr-AdS black hole background exhibit stable trapping, that is, the scalar field remains in a region between the exterior of the black hole and the AdS boundary for a very long time, decaying only inverse logarithmically in time. We study this effect employing fully general simulations that take into account the non-linear backreaction of the scalar field on the geometry. We find that the stable trapping of generic perturbations of Kerr-AdS persists at the non-linear level. Furthermore, the spacetime settles into a time-dependant and non-axisymmetric black hole which differs from Kerr-AdS. Since our perturbations are generic, our results indicate that slowly rotating Kerr-AdS black holes are non-linearly unstable.