Stability of rapidly rotating charged black holes in AdS5 × S5

We study the stability of charged rotating black holes in a consistent truncation of type IIB supergravity on AdS5 × S5 that degenerate to extremal black holes with zero entropy. These black holes have scaling properties between charge and angular momentum similar to those of Fermi surface-like operators in a subsector of N=4 SYM. By solving the equation of motion for a massless scalar field in this background, using matched asymptotic expansion followed by a numerical solution scheme, we are able to compute its quasi-normal modes, and analyze its regime of (in)stability. We find that the black hole is unstable when its angular velocity with respect to the horizon exceeds 1 (in units of 1/lAdS). A study of the relevant thermodynamic Hessian reveals a local thermodynamic instability which occurs at the same region of parameter space. We comment on the endpoints of this instability. (paper)