Topological Photon Spheres of Regular Non-Minimal Magnetic Black Holes

In this paper, we explore the null geodesics of a regular non-minimal magnetic black hole (BH), with a particular emphasis on visualizing photon spheres. This visualization aims to elucidate the dynamics of optically thin accretion around a BH and the resulting observable accretion image from a distant vantage point. Our primary investigation focuses on the fundamental concept that the existence of a photon sphere is an intrinsic feature of spherically symmetric BHs. By introducing the concept of a topological photon sphere, we categorize the behaviors observed in BHs based on the arrangement of their photon spheres. This novel approach not only aids in constraining BH parameters but also facilitates the distinction between a BH and a naked singularity. Moreover, we establish a clear connection between the properties of overall topological charge and effective potential of BH. We observe the scenarios where a stable photon sphere forms without an event horizon by utilizing the effective potential; it could potentially indicate the presence of a naked singularity. However, this would not involve the minima of effective potential lying outside an event horizon, as the event horizon itself would be absent.