Scalar quasi-normal modes of accelerating Kerr-Newman-AdS black holes

Abstract

We study linear scalar perturbations of slowly accelerating Kerr-Newman-anti-de Sitter black holes using the method of isomonodromic deformations. The conformally coupled Klein-Gordon equation separates into two second-order ordinary differential equations with five singularities. Nevertheless, the angular equation can be transformed into a Heun equation, for which we provide an asymptotic expansion for the angular eigenvalues in the small acceleration and rotation limit. In the radial case, we recast the boundary value problem in terms of a set of initial conditions for the isomonodromic tau function of Fuchsian systems with five regular singular points. For the sake of illustration, we compute the quasi-normal modes frequencies.

22 pages, 5 figures, published in JHEP

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• Quasinormal modes of Plebański-Demiański black hole in the near-Nariai regime
• Charged massless scalar fields in a charged $C$-metric black hole: Exact solutions, Hawking radiation, and scattering of scalar waves
• Notes on Quasinormal Modes of charged de Sitter Blackholes from Quiver Gauge Theories
• Connection formulae in the Collision Limit I: Case Studies in Lifshitz Geometry