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

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-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.

13 pages, 6 figures, revised version, accepted for publication in PRD

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• Probing Palatini-type gravity theories through gravitational wave detections via quasinormal modes
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• Static topological black hole with nonminimal derivative coupling and nonlinear electromagnetic field of Born-Infeld type
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