Shadow cast and quasinormal modes in f(R) gravity model inspired by Yang–Mills field

Abstract

In this paper, the null geodesic equations are computed in [Formula: see text] space–time dimensions [Y. Younesizadeh, A. A. Ahmad, A. H. Ahmed, F. Younesizadeh, Ann. Phys. 420, 168246 (2020)] by using the concept of symmetries and Hamilton–Jacobi equation and Carter separable method. With these null geodesics in hand, we evaluate the celestial coordinates (x, y) and the radius [Formula: see text] of the BH shadow and represent it graphically. In addition, we have shown that the peak of this energy slowly shifts to lower frequencies and its height decreases with the increase in the YM magnetic charge ([Formula: see text]) values and decrease in the [Formula: see text] parameter ([Formula: see text]) values. In addition, we have analyzed the concept of effective potential barrier by transforming the radial equation of motion into standard Schrodinger form. The most important result derived from this study is that the height of this potential increases with increase in the YM magnetic charge ([Formula: see text]) values. Then, we study the quasinormal modes (QNMs) of these 4D black holes. For this purpose, we use the WKB approximation method upto third-order corrections. We have shown the perturbation’s decay in corresponding diagrams when the YM magnetic charge ([Formula: see text]) values and the [Formula: see text] parameter ([Formula: see text]) values change.