Quasi-normal modes of the Einstein-Maxwell-aether Black Hole

TL;DR

This paper investigates the quasi-normal modes of charged scalar perturbations in Einstein-Maxwell-aether black holes using multiple numerical methods, revealing consistent results and the existence of quasi-resonances even with large aether parameters.

Contribution

It introduces a specific treatment for the $ ext{-}dependent$ effective potential and a complete numerical procedure for calculating quasi-normal modes in Einstein-Maxwell-aether black holes.

Findings

Consistent results across three numerical methods.

Identification of the allowed parameter region for the black hole.

Existence of quasi-resonances with large aether parameters.

Abstract

We study the quasi-normal modes of the charged scalar perturbations in the background of the Einstein-Maxwell-aether black hole through three methods (WKB method, continued fraction method, generalized eigenvalue method). Then we propose the specific treatment for the generalized effective potential with $\omega$-dependence and the complete procedure of transforming calculation continued fraction method into finding the zero point of the corresponding complex function numerically. These methods are valid because the results from different methods are consistent. We also investigate the allowed region of the second kind aether black hole among the system parameters ($c_{13},c_{14},Q$). Finally we show the existence of quasi-resonances of massive perturbation for Einstein-Maxwell-aether black hole even with large aether parameter.