The Role of Topological Photon Spheres in Constraining the Parameters of Black Holes (2405.06568v1)

Abstract: In this paper, we investigate the topological photon sphere from two distinct perspectives. In the first view, we examine the existence and characteristics of topological photon(anti-photon)spheres for black holes with different structures, such as Einstein-Young-Mills non-minimal, AdS black holes surrounded by Chaplygin-like dark fluid, and Bardeen-like black holes in Einstein-Gauss-Bonnet gravity. Furthermore, we delve into the deeper perspective of the necessity of photon spheres for super-compact gravitational structures such as black holes. By leveraging this necessity, we propose a classification of the parameter space of black hole models based on the existence and positioning of photon spheres. This approach enables the determination of parameter ranges that delineate whether a solution represents a black hole or a naked singularity. In essence, the paper illustrates the utility of the photon sphere as a notable test for establishing the permissible and non-permissible parameter ranges within specific theories of black hole solutions.