Analytic expressions for quasinormal modes and grey-body factors in the eikonal limit and beyond

TL;DR

This paper derives concise analytical expressions for black hole quasinormal modes and grey-body factors that extend beyond the eikonal approximation, demonstrating strong accuracy and providing a general computational approach.

Contribution

It introduces a comprehensive method for deriving analytical expressions for quasinormal modes and grey-body factors beyond the eikonal limit, validated on specific black hole cases.

Findings

Analytical expressions show strong accuracy beyond the eikonal regime.

The approach is applicable to various black hole types, including Schwarzschild-de Sitter and hairy black holes.

A publicly available code facilitates calculations of these expressions.

Abstract

Although the WKB series converges only asymptotically and guarantees the exact result solely in the eikonal regime, we have managed to derive concise analytical expressions for the quasinormal modes and grey-body factors of black holes, expanding beyond the eikonal approximation. Remarkably, these expressions demonstrate unexpectedly strong accuracy. We suggest a comprehensive approach for deriving analytical expressions for grey-body factors and quasinormal modes at various orders beyond the eikonal approximation. Two cases are examined as examples: the Schwarzschild-de Sitter black hole and hairy black holes within the framework of Effective Field Theory. We have publicly shared a generic code that calculates analytical expressions for grey-body factors and quasinormal modes of spherical black holes.