Scalar quasinormal modes of Kerr-AdS${}_5$

Abstract

An analytic expression for the scalar quasinormal modes of the generic, spinning Kerr-$\mathrm{Ad}{\mathrm{S}}_5$ black holes was previously proposed by the authors in ref. 1, in terms of transcendental equations involving the Painlevé 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 both in terms of 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.

JHEP style, 42 pages, 3 figures, 3 tables; Updated discussion on the superradiant modes

References in corpus (5)

• TASI lectures on AdS/CFT
• Maxwell's Equations in the Myers-Perry Geometry
• Superradiant Instability of Five-Dimensional Rotating Charged AdS Black Holes
• Isomonodromy, Painlevé Transcendents and Scattering off of Black Holes
• Holographic Lattices and Numerical Techniques

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