Quasinormal modes and grey-body factors of regular black holes with a scalar hair from the Effective Field Theory

TL;DR

This paper investigates the quasinormal modes and grey-body factors of a regular Hayward black hole with scalar hair within the Effective Field Theory framework, revealing unique overtone behaviors and smaller grey-body factors compared to Schwarzschild black holes.

Contribution

It provides analytical formulas for quasinormal modes in the eikonal regime and explores how overtones and grey-body factors differ from Schwarzschild black holes in this context.

Findings

Overtones deviate significantly from Schwarzschild at higher rates.

Grey-body factors are smaller than those of Schwarzschild black holes.

Late-time tails are indistinguishable from Schwarzschild at late times.

Abstract

The Effective Field Theory (EFT) of perturbations on an arbitrary background geometry with a timelike scalar profile has been recently constructed in the context of scalar-tensor theories. Unlike General Relativity, the regular Hayward metric is realized as an exact background metric in the Effective Field Theory with timelike scalar profile without resorting to special matter field, such as nonlinear electrodynamics. The fundamental quasinormal mode for axial graviational perturbations of this black hole has been considered recently with the help of various methods. Here we make a further step in this direction and find that, unlike the fundamental mode, a few first overtones deviate from their Schwarzschild limit at a much higher rate. This outburst of overtones occurs because the overtones are extremely sensitive to the least change of the near-horizon geometry. The analytical formula for quasinormal modes is obtained in the eikonal regime. In addition, we calculated grey-body factors and showed that the regular Hayward black hole with a scalar hair has a smaller grey-body factor than the Schwarzschild one. Integration of the wave-like equation in the time-domain shows that the power-law tails, following the ring-down phase, are indistinguishable from the Schwarzschild ones at late times.