Dynamical photon spheres in charged black holes and naked singularities

To understand the nature of a black hole shadow in dynamical spacetimes, we construct an analytical model of a dynamical photon sphere in the context of the Bonnor–Vaidya spacetime. Comparing the resulting photon sphere radius with the one in Vaidya spacetime, we find that the charge always decreases the radius of the photon sphere. We also prove that a naked singularity in Bonnor–Vaidya spacetime, unlike the static Reissner–Nordstrom naked singularity, may cast a shadow, and as a result, it cannot be distinguished from a black hole through its shadow.