Vector perturbations of Kerr-AdS5 and the Painleve VI transcendent

We analyze the Ansatz of separability for Maxwell equations in generically spinning, five-dimensional Kerr-AdS black holes. We find that the parameter mu introduced in [1] can be interpreted as apparent singularities of the resulting radial and angular equations. Using isomonodromy deformations, we describe a non-linear symmetry of the system, under which mu is tied to the Painleve VI transcendent. By translating the boundary conditions imposed on the solutions of the equations for quasinormal modes in terms of monodromy data, we find a procedure to fix mu and study the behavior of the quasinormal modes in the limit of fast spinning small black holes.