Quasinormal mode/grey-body factor correspondence for Kerr black holes

TL;DR

This paper develops a systematic WKB-based approach to relate quasinormal modes and greybody factors for Kerr black holes, extending previous work to gravitational perturbations and higher-order corrections.

Contribution

It introduces a new WKB formulation for Kerr black hole perturbations, including gravitational modes and higher-order effects, improving the accuracy of greybody factor predictions.

Findings

Good agreement between predicted and numerical greybody factors at high angular momentum.

Extension of the correspondence to gravitational perturbations.

Identification of the breakdown of the correspondence in the superradiant regime.

Abstract

We revisit the quasinormal-mode/greybody factor correspondence for Kerr black holes in the eikonal limit and develop a systematic WKB-based formulation by recasting the radial Teukolsky equation into a Schr\"odinger-type equation with a short-range potential. Building on earlier studies of the correspondence in rotating backgrounds, we extend the analysis to gravitational perturbations and incorporate higher-order WKB corrections beyond the leading eikonal approximation. For gravitational perturbations, the predicted greybody factors are in good agreement with numerical results obtained from the generalized Sasaki-Nakamura equation, with increasing accuracy at large angular quantum number. We also identify the breakdown of the correspondence in the superradiant regime, where the WKB assumptions cease to be valid.