Instabilities of Kerr-AdS5 x S5 Spacetime

We study gravitational perturbations of the Kerr-AdS(5) x S-5 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-5 and breaks the symmetry SO(6). By taking into account these instabilities, the phase structure of Kerr-AdS(5) x S-5 spacetime is revealed. The implication for the AdS/CFT correspondence is also discussed.