Optical Properties of an Axially Symmetric Black Hole in the Rastall Gravity

This work is devoted to the study of the optical properties of the charged-rotating-NUT-Kiselev (CRNK) black hole in the Rastall theory of gravity. By investigating the motion of photons in the CRNK black hole spacetime in the Rastall gravity we show that the deflection angle of photons due to the gravitational lensing is mostly influenced by the NUT charge, parameter of the equation of state for the quintessence and the quintessential intensity. We observe that the effects of the rest of the spacetime parameters are negligible on the deflection angle. We present the shape of the shadow cast by the CRNK black hole in the Rastall gravity for various values of the spacetime parameters. We demonstrate that spin parameter $a$ of the black hole changes the position and size of the shadow of the black hole very little. While changing the values of the rest of the spacetime parameters can alter the shape and the size of the observed shadow of the black hole significantly. We observe that the radius of the black hole shadow and the deflection angle of a photon are bigger for the CRNK black hole in the Rastall gravity, as compared with the case of the Kerr black hole. Lastly, we show how the spacetime parameters can change the observables $R_s$ and $\delta_s$, being the average radius of the shadow and the distortion parameter that measures the deviation of the shape of the shadow from a perfect circle with radius $R_s$, respectively. Our results show that in most scenarios, for bigger values of $R_s$ we get smaller values of the parameter $\delta_s$.