We study the shadows cast by the different types of rotating regular black holes viz. Ayón-Beato-García (ABG), Hayward, and Bardeen. These black holes have in addition to the total mass ($M$) and rotation parameter ($a$), different parameters as electric charge ($Q$), deviation parameter ($g$), and magnetic charge ($g_{*}$). Interestingly, the size of the shadow is affected by these parameters in addition to the rotation parameter. We found that the radius of the shadow in each case decreases monotonically, and the distortion parameter increases when the values of these parameters increase. A comparison with the standard Kerr case is also investigated. We have also studied the influence of the plasma environment around regular black holes to discuss its shadow. The presence of the plasma affects the apparent size of the regular black hole’s shadow to be increased due to two effects: (i) gravitational redshift of the photons and (ii) radial dependence of plasma density.

The shadow of a rotating non-Kerr black hole has been studied, and it was shown that in addition to the specific angular momentum $a$, the deformation parameter of non-Kerr spacetime essentially deforms the shape of the black hole shadow. For a given value of the black hole spin parameter $a$, the presence of a deformation parameter $ϵ$ reduces the shadow and enlarges its deformation with respect to the one in the Kerr spacetime. Optical features of the rotating non-Kerr black hole in terms of rotation of the polarization vector along null congruences have been studied. A comparison of the obtained theoretical results on the polarization angle with the observational data on Faraday rotation measurements provides the upper limit for the dimensionless deformation parameter as $ϵ\le 19$.

Based on the Newman-Janis algorithm, the Ay\'on-Beato-Garc\'\ia spacetime metric [Phys. Rev. Lett. 80, 5056 (1998)

A large international effort is under way to assess the presence of a shadow in the radio emission from the compact source at the centre of our Galaxy, Sagittarius A* (Sgr A*). If detected, this shadow would provide the first direct evidence of the existence of black holes and that Sgr A* is a supermassive black hole. In addition, the shape of the shadow could be used to learn about extreme gravity near the event horizon and to determine which theory of gravity better describes the observations. The mathematical description of the shadow has so far used a number of simplifying assumptions that are unlikely to be met by the real observational data. We here provide a general formalism to describe the shadow as an arbitrary polar curve expressed in terms of a Legendre expansion. Our formalism does not presume any knowledge of the properties of the shadow, e.g. the location of its centre, and offers a number of routes to characterize the distortions of the curve with respect to reference circles. These distortions can be implemented in a coordinate-independent manner by different teams analysing the same data. We show that the new formalism provides an accurate and robust description of noisy observational data, with smaller error variances when compared to previous approaches for the measurement of the distortion.

We have studied photon motion around axially symmetric rotating Kerr black holes in the presence of a plasma with radial power-law density. It is shown that in the presence of a plasma, the observed shape and size of the shadow changes depending on the (i) plasma parameters, (ii) black hole spin, and (iii) inclination angle between the observer plane and the axis of rotation of the black hole. In order to extract the pure effect of the plasma influence on the black hole image, the particular case of the Schwarzschild black hole has also been investigated and it has been shown that the photon sphere around the spherically symmetric black hole is left unchanged under the plasma influence; however, the Schwarzschild black hole shadow size in the plasma is reduced due to the refraction of the electromagnetic radiation in the plasma environment of the black hole. The study of the energy emission from the black hole in plasma environment shows that in the presence of the plasma the maximal energy emission rate from the black hole decreases.