Shadow and observational constraints of dynamic phantom black holes

In this study, we investigate the shadow of dynamic Phantom black hole (BH) and their observable implications with actual images of the BHs M87* and SgrA. Using the Hamilton–Jacobi formalism, we derive the null geodesic equations within the symmetry planes of spacetime, which facilitates the precise calculation of the radius of the BH shadow and its celestial coordinates. One can notice that the BH shadow’s radius exhibits a notable dependence on the BHs electric charge e and magnetic charge g. We observe that the magnetic charge g has a distinct effect on the shadow’s radius [Formula: see text] for the [Formula: see text] BH spacetime compared to the asymptotically flat BH spacetime. For both spacetime configurations, an increase in the magnetic charge g correlates with an enlargement of the BH shadow’s radius. Furthermore, we introduce a plasma medium to assess the shadow’s sensitivity to variations in the plasma refractive index. This approach allows us to simulate the optical properties of the surrounding environment and its effect on the perceived size of the BH shadow. In addition, we examine how the magnetic charge affects the BHs energy emission rate, drawing a correlation with the shadow’s dimensions. We also compare the theoretical depiction of BH images with the actual images of M87* and SgrA*.