Quasinormal modes of a small Schwarzschild–anti-de Sitter black hole

Abstract

We compute the quasinormal modes associated with the decay of the massless scalar field around a small Schwarzschild--anti-de Sitter black hole. The computations show that when the horizon radius is much less than the anti--de Sitter radius, the imaginary part of the frequency goes to zero as ${r}_{+}^{d\ensuremath{-}2}$ while the real part of $\ensuremath{\omega}$ decreases to its minimum and then goes to $d\ensuremath{-}1.$ Thus the quasinormal modes approach the usual AdS modes in the limit ${r}_{+}\ensuremath{\rightarrow}0.$ This agrees with suggestions of Horowitz and Hubeny [Phys. Rev. D 62, 024027 (2000)].