Black holes with multiple photon spheres

Recently, asymptotically flat black holes with multiple photon spheres have been discovered and found to produce distinctive observational signatures. In this paper, we focus on whether these black hole solutions are physically viable, e.g., satisfying energy conditions of interest. Intriguingly, black hole and naked singularity solutions with two photon spheres and one antiphoton sphere are shown to exist in physically reasonable models, which satisfy the null, weak, dominant and strong energy conditions. Our findings reveal that black holes with multiple photon spheres may not be frequent, but they are not exotic.