Quasinormal frequencies of a massless scalar in the hidden Kerr/CFT proposal

TL;DR

This paper demonstrates that the hidden Kerr/CFT symmetry can be used to algebraically determine the quasinormal frequencies of massless scalar waves in Kerr black holes, especially near-extremal ones, with approximate accuracy.

Contribution

It shows that the hidden conformal symmetry near the horizon allows for an algebraic calculation of quasinormal frequencies for scalar perturbations in Kerr black holes.

Findings

QNFs match those of near-horizon scalar perturbations in NEK black holes

The method applies to non-equatorial scalar modes

Approximate determination of QNFs using hidden symmetry

Abstract

The hidden Kerr/CFT proposal implies that the massless scalar wave equation in the near-region and low-frequency limit respects a hidden SL(2,R)$\times$SL(2,R) invariance in the Kerr black hole spacetime. We may use this symmetry to determine quasinormal frequencies (QNFs) of the massless scalar wave propagating around the Kerr black hole algebraically. It is shown that QNFs obtained using the hidden conformal symmetry near the horizon correspond approximately to not only those of scalar perturbation around the near-horizon region of a nearly extremal Kerr (NEK) black hole, but also those of non-equatorial scalar modes around the NEK black hole. This indicates that the hidden Kerr/CFT proposal could determine quasinormal modes and frequencies of the massless scalar wave around the NEK (rapidly rotating) black hole approximately.