Scalar perturbations of Kerr-AdS black holes

We numerically study the scalar perturbation of a rotating black hole in anti--de Sitter spacetime (Kerr-AdS black hole). It is found that small Kerr-AdS black holes characterized by ${r}_{+}\ensuremath{\lesssim}0.16\ensuremath{\ell}$ are unstable against scalar perturbations via the superradiant amplification mechanism for some rotation rates, where ${r}_{+}$ and $\ensuremath{\ell}$ stand, respectively, for the radial coordinate value of the black hole event horizon in the Boyer-Lindquist coordinates and the cosmological length-scale, defined by $\ensuremath{\ell}=(\ensuremath{-}3/\ensuremath{\Lambda}{)}^{1/2}$. Here $\ensuremath{\Lambda}$ is the (negative) cosmological constant.