Correspondence between quasinormal modes and grey-body factors of Schwarzschild--Tangherlini black holes

TL;DR

This paper explores the relationship between quasinormal modes and grey-body factors of higher-dimensional Schwarzschild--Tangherlini black holes, analyzing the accuracy and limitations of their correspondence across different perturbation types and dimensions.

Contribution

It provides a detailed analysis of the correspondence's validity for various perturbation modes and dimensions, highlighting where it holds and where it breaks down.

Findings

Good correspondence for vector and tensor perturbations across all dimensions.

Failure of the correspondence for scalar perturbations with l=2 in dimensions D≥7.

Breakdown of the correspondence is due to multiple potential barriers.

Abstract

We investigate the correspondence between the quasinormal modes and grey-body factors of Schwarzschild--Tangherlini black holes. The gravitational perturbations in higher-dimensional black holes can be classified into scalar, vector, and tensor types. Considering the dimension-dependent forms of their effective potentials, the correspondence was examined for each dimension and perturbation mode. The accurate quasinormal modes were computed by suitably adopting the continued fraction and integration-through-midpoints methods, depending on the structure of the singularity. The grey-body factor can be obtained through its correspondence with the quasinormal mode, and its accuracy was analyzed by calculating its difference from the numerically computed grey-body factor. The correspondence failed for $l=2$ scalar gravitational perturbations in $D\ge7$ because the form of the potential is markedly different from that in four dimensions. The vector and tensor perturbation types exhibited good correspondence accuracies in all cases. The breakdown of the correspondence was rigorously demonstrated to stem from multiple potential barriers, and its applicability to each mode in higher dimensions was assessed.