Black hole shadows of massive particles and photons in plasma

Explicitly covariant analytical expressions are derived that describe the boundaries of shadows cast by massive particles scattered by a gravitating object. This covers scenarios with particles having effectively variable mass, such as photons in plasma, geodesics in higher dimensions, and particles interacting with a scalar field. The derived formula takes advantage of recent advances in understanding the relationship between slice-reducible Killing tensors and massive particle surfaces that generalize photon surfaces. The formula allows us to obtain simple approximations of scaling as the particle energy changes. We illustrate this structure using Kerr-NUT and EMD black holes for both massive particles and photons in plasma. The versatility of this framework extends beyond astrophysics and has potential applications in analog models of gravity and condensed matter physics.