Superradiance and dynamical evolution of a charged scalar field in an asymptotically anti–de-Sitter dilatonic black hole

Abstract

We study the dynamics of charged massless scalar fields in asymptotically anti–de Sitter (AdS) dilatonic black holes. The instability of the scalar field, which is triggered by the charged superradiant effect and Dirichlet boundary condition at AdS spatial infinity, can be notably described by exponential growth of the scalar field amplitude in time evolving and unstable quasinormal modes of scalar field perturbation. The numerical computation to demonstrate the superradiant instability of the charged scalar field are performed in the time domain and frequency domain, respectively. We confirm the mode that dominates long time behavior of scalar field matches with quasinormal mode obtained from frequency domain analysis quite well. It is well known the small Reissner-Nordstrom-anti–de Sitter (RN-AdS) black holes are superradiant unstable, while the large RN-AdS black holes are stable against the charged scalar perturbations. According to our numerical results, it is observed that the large dilatonic AdS black holes are also superradiant unstable. At last, we conclude that there exist rapid exponential growing superradiant modes in charged dilatonic AdS black holes, which is significant for the nonlinear dynamical evolution of charged superradiant instability.