Quasi-normal modes of massless scalar fields for charged black holes in the Palatini-type gravity

TL;DR

This paper investigates the quasi-normal modes of massless scalar fields around various charged black holes in Palatini-type gravity theories, revealing how modifications in gravity and matter sectors influence the QNM spectra.

Contribution

It provides the first detailed analysis of QNMs for charged black holes in Palatini $f(R)$ and EiBI gravity theories, including stability and frequency calculations.

Findings

Charged black holes in these theories are stable.

QNM frequencies differ from Reissner-Nordström black holes due to gravity and matter modifications.

Eikonal limit frequencies are also computed and compared.

Abstract

The scrutiny of black hole perturbations and its application to testing gravity theories have been a very crucial frontier in modern physics. In this paper we study the quasi-normal modes (QNM) of massless scalar perturbations for various charged black holes in the Palatini-type theories of gravity. Specifically, we consider the Palatini $f(R)$ theory coupled with Born-Infeld nonlinear electrodynamics and the Eddington-inspired-Born-Infeld gravity (EiBI) coupled with Maxwell electromagnetic fields. Special attention is paid to Einstein-Born-Infeld black holes, EiBI charged black holes and Born-Infeld charged black holes within $R\pm R^2$ gravity. These charged black holes are shown to be stable and their quasi-normal frequencies, including the frequencies in the eikonal limit, are calculated by using the WKB method up to the 6th order. We compare the results with the Reissner-Nordstr\"om charged black hole and prove that both the changes in the gravity sector and the matter sector of the action alter the QNM spectra.