Quasinormal modes of Schwarzschild–anti-de Sitter black holes: Electromagnetic and gravitational perturbations

We study the quasinormal modes (QNM) of electromagnetic and gravitational perturbations of a Schwarzschild black hole in an asymptotically anti--de Sitter (AdS) spacetime. Some of the electromagnetic modes do not oscillate; they only decay, since they have pure imaginary frequencies. The gravitational modes show peculiar features: the odd and even gravitational perturbations no longer have the same characteristic quasinormal frequencies. There is a special mode for odd perturbations whose behavior differs completely from the usual one in scalar and electromagnetic perturbations in AdS spacetime, but has a similar behavior to the Schwarzschild black hole in an asymptotically flat spacetime: the imaginary part of the frequency goes as ${1/r}_{+},$ where ${r}_{+}$ is the horizon radius. We also investigate the small black-hole limit showing that the imaginary part of the frequency goes as ${r}_{+}^{2}.$ These results are important to the AdS/CFT conjecture since, according to it, the QNM's describe the approach to equilibrium in the conformal field theory.