Kerr-AdS and its Near-horizon Geometry: Perturbations and the Kerr/CFT Correspondence

TL;DR

This paper studies linear perturbations of Kerr-AdS black holes and their near-horizon geometries, finding no instabilities and highlighting implications for the Kerr/CFT correspondence.

Contribution

It provides explicit solutions for perturbations in NHEK-AdS and examines stability, revealing violations of Kerr/CFT fall-off conditions except for axisymmetric cases.

Findings

No non-axisymmetric instabilities found.

Perturbation behavior challenges Kerr/CFT boundary conditions.

Stability properties align with near-horizon conjectures.

Abstract

We investigate linear perturbations of spin-s fields in the Kerr-AdS black hole and in its near-horizon geometry (NHEK-AdS), using the Teukolsky master equation and the Hertz potential. In the NHEK-AdS geometry we solve the associated angular equation numerically and the radial equation exactly. Having these explicit solutions at hand, we search for linear mode instabilities. We do not find any (non-)axisymmetric instabilities with outgoing boundary conditions. This is in agreement with a recent conjecture relating the linearized stability properties of the full geometry with those of its near-horizon geometry. Moreover, we find that the asymptotic behaviour of the metric perturbations in NHEK-AdS violates the fall-off conditions imposed in the formulation of the Kerr/CFT correspondence (the only exception being the axisymmetric sector of perturbations).