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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 q=1, 2,. . .: pₑ=- c^2 (2q-1) ^-1, pₓ=-pₑ, where is the mass density, c is the speed of light, pₑ and pₓ are pressures in the radial and transverse directions, respectively. Circular null geodesics are explored, and a master equation for the radius r* of a photon sphere is found, as well as the proposition on the existence and uniqueness of a solution to the master equation, obeying r*>r₇, where r₇ 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.
Иващук et al. (Mon,) studied this question.