Reply to "On the branching of quasinormal resonances of near-extremal Kerr black holes" by Shahar Hod

TL;DR

This paper refutes the existence of certain high-spin quasinormal modes in near-extremal Kerr black holes, clarifying the mode spectrum bifurcation and correcting previous claims of additional damped modes.

Contribution

It provides a critical analysis that dismisses the proposed high-spin damped modes, clarifies the mode bifurcation in near-extremal black holes, and corrects earlier theoretical derivations.

Findings

No evidence for the proposed high-spin damped modes.

Confirmation of the bifurcation of quasinormal modes.

Identification of an inconsistency in previous mode derivations.

Abstract

In a study of the quasinormal mode frequencies of nearly extremal black holes, we pointed out a bifurcation of the mode spectrum into modes with finite decay and modes with vanishing decay in the extremal limit. We provided analytic and semi-analytic results identifying which families of modes bifurcated, and when modes with finite decay rates exist when approaching the extremal limit. In a recent note (arXiv:1510.05604), Hod suggests that additional modes asymptote to finite decay at extremely high spin parameter, based on past work by Detweiler. We search for these suggested modes and find no evidence of their existence. In addition, we point out an inconsistency in the derivation of the proposed modes, which further indicates that these damped modes do not exist.