Scalar quasinormal modes of Kerr-AdS5

Abstract

An analytic expression for the scalar quasinormal modes of generic, spinning Kerr-AdS5 black holes was previously proposed by the authors [J. High Energy Phys. 08 (2017) 094JHEPFG1029-847910.1007/JHEP08(2017)094], in terms of transcendental equations involving the Painlevé VI (PVI) τ function. In this work, we carry out a numerical investigation of the modes for generic rotation parameters, comparing implementations of expansions for the PVI τ 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.