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

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-2 while the real part of decreases to its minimum and then goes to d-1. Thus the quasinormal modes approach the usual AdS modes in the limit r+0. This agrees with suggestions of Horowitz and Hubeny Phys. Rev. D 62, 024027 (2000).