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Reissner-Nordstr\"om Anti-de Sitter (RNAdS) black holes are unstable againstthe charged scalar field perturbations due to the well-known superradiancephenomenon. We present the time domain analysis of charged scalar fieldperturbations in the RNAdS black hole background in general dimensions. We showthat the instabilities of charged scalar field can be explicitly illustratedfrom the time profiles of evolving scalar field. By using the Prony method tofit the time evolution data, we confirm the mode that dominates the long timebehavior of scalar field is in accordance with the quasinormal mode from thefrequency domain analysis. The superradiance origin of the instability can alsobe demonstrated by comparing the real part of the dominant mode with thesuperradiant condition of charged scalar field. It is shown that all theunstable modes are superradiant, which is consistent with the analytical resultin the frequency domain analysis. Furthermore, we also confirm there exists therapid exponential growing modes in the RNAdS case, which makes the RNAdS blackhole a good test ground to investigate the nonlinear evolution of superradiantinstability.

Time evolutions of scalar field perturbations in $D$-dimensional Reissner-Nordstr\"om Anti-de Sitter black holes