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 quasinormal 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 Wentzel-Kramers-Brillouin (WKB) method up to the 6th order. We compare the results with the Reissner-Nordström charged black hole and prove that both the changes in the gravity sector and the matter sector of the action alter the QNM spectra.

• Received 29 June 2018

DOI:https://doi.org/10.1103/PhysRevD.98.044042