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It is now established that small Kerr-Anti-de Sitter (Kerr-AdS) black holesare unstable against scalar perturbations, via superradiant amplificationmechanism. We show that small Kerr-AdS black holes are also unstable againstgravitational perturbations and we compute the features of this instability. Wealso describe with great detail the evolution of this instability. Inparticular, we identify its endpoint state. It corresponds to a Kerr-AdS blackhole whose boundary is an Einstein universe rotating with the light velocity.This black hole is expected to be slightly oblate and to co-exist inequilibrium with a certain amount of outside radiation.Comment: 11 pages, RevTex4. v2: small typos corrected. Version to appear in  Phys. Rev.

Classical instability of Kerr-AdS black holes and the issue of final state