Quasinormal behavior of massless scalar field perturbation in Reissner-Nordström anti-de Sitter spacetimes

We present a comprehensive study of the massless scalar field perturbation in the Reissner-Nordstr\"om anti-de Sitter (RNAdS) space-time and compute its quasinormal modes (QNM). For the lowest lying mode, we confirm and extend the dependence of the QNM frequencies on the black hole charge obtained in previous works. In near extreme limit, under the scalar perturbation we find that the imaginary part of the frequency tends to zero, which is consistent with the previous conjecture based on electromagnetic and axial gravitational perturbations. For the extreme value of the charge, the asymptotic field decay is dominated by a power-law tail, which shows that the extreme black hole can still be stable to scalar perturbations. We also study the higher overtones for the RNAdS black hole and find large variations of QNM frequencies with the overtone number and black hole charge. The nontrivial dependence of frequencies on the angular index is also discussed.