Vector perturbations of Kerr-AdS${}_5$ and the Painlevé VI transcendent

Abstract

We analyze the Ansatz of separability for Maxwell equations in generically spinning, five-dimensional Kerr-AdS black holes. We find that the parameter μintroduced in a previous work by O. Lunin 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 μis tied to the Painlevé 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 μand study the behavior of the quasinormal modes in the limit of fast spinning small black holes.

Minor comments on fixing of parameters and polarizations, 31 pages, 2 figures, JHEP style

References in corpus (5)

• Massive Vector Fields in Rotating Black-Hole Spacetimes: Separability and Quasinormal Modes
• Instability of the Proca field on Kerr spacetime
• Maxwell's Equations in the Myers-Perry Geometry
• Separation of Maxwell equations in Kerr-NUT-(A)dS spacetimes
• Principal Tensor Strikes Again: Separability of Vector Equations with Torsion

Cited by in corpus (2)

• Remarks on holographic models of the Kerr-AdS${}_5$ geometry
• Circular strings in Kerr-$Ad{S}_5$ black holes