  We investigate the decay of a scalar field outside a Schwarzschild anti de
Sitter black hole. This is determined by computing the complex frequencies
associated with quasinormal modes. There are qualitative differences from the
asymptotically flat case, even in the limit of small black holes. In
particular, for a given angular dependence, the decay is always exponential -
there are no power law tails at late times. In terms of the AdS/CFT
correspondence, a large black hole corresponds to an approximately thermal
state in the field theory, and the decay of the scalar field corresponds to the
decay of a perturbation of this state. Thus one obtains the timescale for the
approach to thermal equilibrium. We compute these timescales for the strongly
coupled field theories in three, four, and six dimensions which are dual to
string theory in asymptotically AdS spacetimes.
