Axial gravitational quasi-normal modes of spherically symmetric black hole in f(R) gravity and its optical appearance

This paper investigates the axial gravitational perturbations originating from spherically symmetric black holes in f ( R ) gravity, along with the optical appearance of such a black hole. The aim is to search for evidence of the existence of these black holes in astrophysical observations and thereby test the correctness of the f ( R ) theory. In literature Kalita and Mukhopadhyay (Eur Phys J C 79:877, 2019), the spherically symmetric black hole metric in f ( R ) gravity is obtained. By comparing it with the metric for spherically symmetric black holes in general relativity, we find that the modification of gravity due to f ( R ) can be described in this black hole spacetime using a parameter C f . Next, we study axial gravitational perturbations in this spacetime and successfully derive a decoupled axial perturbation equation. We also discuss the impact of f ( R ) gravity on the quasi-normal mode frequencies. Additionally, we have also investigated the optical appearance of the black hole. We discuss the impact of the parameter C f on the observable characteristics of the accretion disk. In principle, both of these effects can be observed using gravitational wave detectors and astronomical telescopes.