Photon Spheres near Black Holes in a Model with an Anisotropic Fluid

Abstract: This semi-review paper studies null geodesics which exist for black hole solutions in a gravitational 4D model with an anisotropic fluid. The equations of state for the fluid and the solutions depends on the integer parameter :, where is the mass density, is the speed of light, and are pressures in the radial and transverse directions, respectively. Circular null geodesics are explored, and a master equation for the radius of a photon sphere is found, as well as the proposition on the existence and uniqueness of a solution to the master equation, obeying, where is the horizon radius. Relations for the spectrum of quasinormal modes for a test massless scalar field in the eikonal approximation are overviewed and compared with the cyclic frequencies of circular null geo desics. Shadow angles are explored. © Pleiades Publishing, Ltd. 2025.