Plasma Effects on the Shadow of a Rotating Black Hole in Asymptotically Safe Gravity

We investigate the shadow of a rotating black hole in the infrared limit of asymptotically safe gravity (ASG), focusing on how different plasma distributions affect photon propagation and shadow properties. Using the Hamilton–Jacobi formalism, we derive the photon equations of motion in plasma and calculate the shadow boundary for three different plasma distributions. Relative to the case without plasma, a homogeneous plasma increases the shadow size, whereas radially and angularly inhomogeneous plasma distributions reduce it. The inhomogeneous plasma models make the shadow more circular, whereas the effect of a homogeneous plasma on the shadow shape depends on the ASG parameter ξ˜. The angularly inhomogeneous plasma has a stronger effect on the shadow size, whereas the radially inhomogeneous plasma has a greater influence on the shadow shape. For fixed plasma parameters, increasing ξ˜ reduces the shadow size and increases its departure from circularity. Overall, plasma has a more pronounced effect on the shadow size than on its shape. Finally, we use the EHT observations of Sgr A* to constrain the (ξ˜,Kr) parameter space for the radially inhomogeneous plasma model. Under the conditions adopted in this work, the EHT observations mainly disfavor regions where both ξ˜ and Kr take relatively large values.