Quasinormal Modes of Dilaton Black Holes: Analytic approximations

TL;DR

This paper derives accurate analytic formulas for quasinormal modes of scalar and Dirac fields in dilaton black holes using higher-order WKB expansion, improving upon previous numerical methods and confirming the null geodesic correspondence in the eikonal limit.

Contribution

It provides the first high-precision analytic expressions for quasinormal modes in dilaton black holes using advanced WKB techniques.

Findings

Analytic formulas outperform previous numerical results.

In the eikonal regime, quasinormal modes follow null geodesic correspondence.

Higher-order WKB yields more accurate results than lower-order approximations.

Abstract

We have derived precise analytic expressions for the quasinormal modes of test scalar, and Dirac fields in the background of the dilaton black hole. To achieve this, we employ the higher-order WKB expansion in terms of $1/\ell$. A comparison between the analytic formulas and time-domain integration reveals that the analytic approach generally yields more accurate results than the numerical results previously published using the lower-order WKB approach. We demonstrate that in the eikonal regime, test fields adhere to the correspondence between null geodesics and eikonal quasinormal modes.