We study gravitational perturbations of the Kerr-AdS5 × S5 spacetime with equal angular momenta. In this spacetime, we found the two types of classical instability, superradiant and Gregory-Laflamme. The superradiant instability is caused by the wave amplification via superradiance and by wave reflection due to the potential barrier of the AdS spacetime. The Gregory-Laflamme instability appears in Kaluza-Klein modes of the internal space S and breaks the symmetry SO(6). By taking into account these instabilities, the phase structure of Kerr-AdS5 x S5 spacetime is revealed. The implication for the AdS/CFT correspondence is also discussed.
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