Shadow and weak gravitational lensing of a rotating regular black hole in a non-minimally coupled Einstein-Yang-Mills theory in the presence of plasma

Abstract: The null geodesics of the regular and rotating magnetically charged black hole in a non-minimally coupled Einstein-Yang-Mills theory surrounded by a plasma medium is studied. The effect of magnetic charge and Yang-Mills parameter on the effective potential and radius of photon orbits has investigated. We then study the shadow of a regular and rotating magnetically charged black hole along with the observables in presence of the plasma medium. The presence of plasma medium affects the apparent size of the shadow of a regular rotating black hole in comparison to vacuum case. Variation of shadow radius and deformation parameter with Yang-Mills and plasma parameter has examined. Furthermore, the deflection angle of the massless test particles in weak field approximation around this black hole spacetime in presence of homogeneous plasma medium is also investigated. Finally, we have compared the obtained results with Kerr-Newman and Schwarzschild black hole solutions in general relativity (GR).