Correspondence between grey-body factors and quasinormal modes

TL;DR

This paper explores an approximate link between grey-body factors and quasinormal modes of black holes, especially in the high-frequency regime, revealing insights into their spectral relationship and stability properties.

Contribution

It establishes an approximate correspondence between grey-body factors and quasinormal modes, becoming exact at high frequencies, and explains their spectral connection and stability differences.

Findings

Grey-body factors can be expressed via fundamental quasinormal modes in the eikonal regime.

The correspondence is exact in the high-frequency limit.

Grey-body factors are less sensitive to potential deformations than overtones.

Abstract

Quasinormal modes and grey-body factors are spectral characteristics corresponding to different boundary conditions: the former imply purely outgoing waves to the event horizon and infinity, while the latter allow for an incoming wave from the horizon, thus describing a scattering problem. Nevertheless, we show that there is a link between these two characteristics. We establish an approximate correspondence between the quasinormal modes and grey-body factors, which becomes exact in the high-frequency (eikonal) regime. We show that, in the eikonal regime, the grey-body factors of spherically symmetric black holes can be remarkably simply expressed via the fundamental quasinormal mode, while at smaller $\ell$, the correction terms include values of the overtones. This might be interesting in the context of the recently observed connection between grey-body factors and the amplitudes of gravitational waves from black holes. The correspondence might explain why grey-body factors are more stable, i.e. less sensitive, than higher overtones to small deformation of the effective potential.