Null orbits and shadows in the Ernst-Wild geometry: insights for black holes immersed in a magnetic field

We investigate the null geodesics, in particular the stable and unstable light rings and shadows, of a Kerr-Newman black hole immersed in an asymptotically uniform magnetic field as described by the Ernst-Wild (Melvin-Kerr-Newman) spacetime. Through numerical ray tracing, we demonstrate that both the black hole rotation and the magnetized Melvin geometry impact the light rings and shadows non-trivially and in compensating ways. In addition, we use a perturbative expansion in the magnetic field B to analyze the deviation of the observable shadow relative to the Kerr result analytically, and determine connections between Lyapunov exponents for light ring instabilities and quasinormal modes in the eikonal limit.