Shadow of a charged rotating black hole in f(R) gravity

Abstract

A charged rotating black hole in f(R) gravity is characterized by mass, M, spin, a, electric charge, Q, and $R_{0}$ which is proportional to cosmological constant. We analyze the image of the black hole shadow in four types (1) at $r\rightarrow \infty$, (2) at $r\rightarrow r_{O}$ in vacuum, (3) at $r\rightarrow \infty$ and (4) at $r\rightarrow r_{O}$ for an observer at the presence of plasma. Moreover, we investigate the effect of spin, charge, and modification of gravity on the shape of the shadow. In addition, we use two observable parameters, the radius $R_{s}$ and the distortion parameter $\delta _{s}$, characterizing the apparent shape. We show that the shadow becomes smaller with increasing electric charge for all cases. Also, by increasing the rotation parameters, the circular symmetry of the black hole’s shadow image will change. Furthermore, in the presence of plasma, the plasma parameter also affects the size of the shadow.

Appendix

Table 1 The details of parameter in Fig. 1, for an observer at infinity, the Q and a parameter were investigated in this figure in vacuum

Table 2 The details of parameter in Figs. 4, 5, and 6, for an observer at limited distance, effect of spin parameter, a were investigated in this figure in vacuum

Table 3 The details of parameter in Fig. 8, for an observer at limited distance

Table 4 The details of parameter in Fig. 9 for an observer at $\infty$, the effect of a and Q, were investigated in this figure in the presence of plasma

Table 5 The details of parameter in Fig. 11, the effect of spin parameter, a for an observer at limited distance in the presence of plasma

Table 6 The details of parameter in Fig. 12, the effect of electric charge parameter, Q for an observer at limited distance in the presence of plasma