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 $\omega$ decreases to its minimum and then goes to $d-1.$ Thus the quasinormal modes approach the usual AdS modes in the limit $r_{+}\to 0.$ This agrees with suggestions of Horowitz and Hubeny [Phys. Rev. D 62, 024027 (2000)].

• Received 16 May 2002

DOI:https://doi.org/10.1103/PhysRevD.66.044009