Scalar quasinormal modes of Kerr-AdS(5)

An analytic expression for the scalar quasinormal modes of generic, spinning Kerr-AdS(5) black holes was previously proposed by the authors [J. High Energy Phys. 08 (2017) 094], in terms of transcendental equations involving the Painlev'e VI (PVI) tau function. In this work, we carry out a numerical investigation of the modes for generic rotation parameters, comparing implementations of expansions for the PVI tau function in terms of both conformal blocks (Nekrasov functions) and Fredholm determinants. We compare the results with standard numerical methods for the subcase of Schwarzschild black holes. We then derive asymptotic formulas for the angular eigenvalues and the quasinormal modes in the small black hole limit for generic scalar mass and discuss, both numerically and analytically, the appearance of superradiant modes.