Analytic expressions for grey-body factors of the general parametrized spherically symmetric black holes

TL;DR

This paper derives analytic formulas for grey-body factors of general spherically symmetric black holes, showing their dependence on horizon deviations and stability against near-horizon deformations.

Contribution

It provides new analytic expressions for grey-body factors of parametrized black holes, highlighting the dominant role of horizon radius deviations.

Findings

Grey-body factors are mainly influenced by the horizon radius deviation.

The formulas are accurate for small deviations from Schwarzschild geometry.

Grey-body factors are more stable than quasinormal modes under near-horizon changes.

Abstract

In light of the recently discovered connection between grey-body factors and quasinormal ringing, we derive analytic expressions for the grey-body factors of generic parametrized spherically symmetric and asymptotically flat black holes. These expressions are presented as expansions in terms of the inverse multipole number and the coefficients of the parametrization. The obtained analytic formulas serve as good approximations whenever the deviation from the Schwarzschild geometry is not very large. We demonstrate that the primary parameter determining the grey-body factors is the deviation of the event horizon radius from its Schwarzschild value, while the higher-order coefficients of the parametrization, which govern the near-horizon geometry, are much less significant. This finding is consistent with recent observations that grey-body factors are considerably more stable against small deformations of the near-horizon geometry than quasinormal modes.