Gravitational instability of simply rotating Myers-Perry-AdS black holes

We study the stability of a higher-dimensional AdS black hole rotating in a single two plane for tensor-type gravitational perturbations. We first show by an analytic method that there exists no unstable mode when the magnitude $a$ of the angular momentum is smaller than $r_h^2/R$ where $r_h$ is the horizon radius, and $R$ is the AdS curvature radius. Then, by numerical calculations of quasinormal modes utilizing the separability of the relevant perturbation equation, we show that instability occurs for rapidly rotating black holes with $aR>r_h^2$, although the growth rate is tiny, yet detectable. We give numerical evidences indicating that this instability is caused by superradiance.