Remarks on holographic models of the Kerr-AdS$_{5}$ geometry

TL;DR

This paper investigates scalar perturbations of Kerr-AdS5 black holes at low temperatures using isomonodromic techniques, revealing stability of fundamental modes and superradiance of excited modes, with implications for holography.

Contribution

It introduces a novel application of isomonodromic methods to analyze low-temperature perturbations in Kerr-AdS5 black holes, connecting monodromy parameters to Painlevé V transcendent expansions.

Findings

Fundamental mode remains perturbatively stable at low temperatures.

Excited modes exhibit superradiance, consistent with thermodynamics.

Numerical analysis confirms low-lying frequency behavior.

Abstract

We study the low-temperature limit of scalar perturbations of the Kerr-AdS$_{5}$ black-hole for generic rotational parameters. We motivate the study by considering real-time holography of small black hole backgrounds. Using the isomonodromic technique, we show that corrections to the extremal limit can be encoded in the monodromy parameters of the Painlev\'e V transcendent, whose expansion is given in terms of irregular chiral conformal blocks. After discussing the contribution of the intermediate states to the quasi-normal modes, we perform a numerical analysis of the low-lying frequencies. We find that the fundamental mode is perturbatively stable at low temperatures for small black holes and that excited perturbations are superradiant, as expected from thermodynamical considerations. We close by considering the holographic interpretation of the unstable modes and the decaying process.