  We study the stability of charged rotating black holes in a consistent
truncation of Type $IIB$ Supergravity on $AdS_5 \times S^5$ 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 ${\cal N}=4$ 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 it's 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 $1/l_{AdS}$). 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.
