# Scalar quasinormal modes of Kerr-AdS$\mathbf{_5}$

## TL;DR

This paper numerically investigates scalar quasinormal modes of Kerr-AdS5 black holes, compares methods for computing them, and explores asymptotic behaviors and superradiance phenomena.

## Contribution

It provides a detailed numerical analysis of the Painlevé VI tau function approach and derives asymptotic formulas for modes in the small black hole limit.

## Key findings

- Numerical results for quasinormal modes across rotation parameters.
- Validation of Painlevé VI tau function methods against standard techniques.
- Identification of superradiant modes in the small black hole regime.

## Abstract

An analytic expression for the scalar quasinormal modes of the generic, spinning Kerr-$\mathrm{AdS_5}$ black holes was previously proposed by the authors in ref. 1, 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 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.