Deflection Light Behaviors by AdS Black Holes

We investigate the behavior of the deflection of light rays by charged and rotating AdS black holes using the Gauss-Bonnet formalism. Taking weak field approximations and certain appropriate limits associated with AdS geometries, we compute and analyze such an optical quantity by varying the involved moduli space parameters. First, we study the charge and the AdS radius effects on the deflection angle of RN-AdS black holes. For small values of the impact parameter \(b\), we find that the charge effect is relevant. Precisely, it decreases the deflection angle, while the AdS background one is not. For large values of \(b\), however, these optical behaviors have been inverted and the deflection angle becomes an increasing function of the charge. In this way, the cosmological constant effect is remarked to be relevant showing linear variations of the deflection angle. Varying the charge, we find a critical impact parameter value \(b_{c}\) where the charge effect is inverted. For rotating solutions, we show that the spinning parameter still decreases the deflection angle without any changing behavior observed in the charge effect. Evincing of the cosmological constant, we recover known results corresponding to charged and rotating ordinary black hole solutions. Examining the plasma effect, we reveal that the deflection angle keeps the same behavior being a decreasing function in terms of the frequency ratio.