Probing the Starobinsky-Bel-Robinson gravity by photon motion around the Kerr-type black hole in non-uniform plasma

Abstract

This study investigates the optical properties of a rotating black hole in Starobinsky-Bel-Robinson gravity, characterized by the additional parameter β. The black hole is assumed to be surrounded by non-uniform plasma, with the plasma parameter k describing its effect on photon motion. The results reveal that the influence of the β parameter on the photon motion is significant near the black hole and it becomes weak at larger distances from the black hole. The deflection angle of photons for gravitational lensing which depends on the spin of the black hole demonstrates monotonic decrease with increase in the value of the plasma parameter k. The presence of the β parameter leads to a maximum deflection angle near the black hole, which decreases with increasing photon distance from the horizon of the black hole. The photon sphere radius is strongly affected by the β parameter and by the black hole spin, but weakly influenced by the plasma parameter. The shadow cast by the black hole which is altered by the β parameter, deformed on the left-hand side. Increase in the value of the plasma parameter k reduces the shadow size of the black hole. The effect of the spin on the shadow size is observed when β takes comparatively bigger values. The average shadow radius is affected by the spacetime parameters and plasma parameter, exhibiting a non-monotonic behavior with increasing β. The distortion of shadow of the black hole is influenced by the parameter β in a considerable and non-monotonic manner. Observational constraints for Sgr A* show our model aligns within confidence bounds but falls short of upper limits, revealing shadow radius limitations.