The optical features of noncommutative charged 4D-AdS-Einstein–Gauss–Bonnet black hole: shadow and deflection angle

In this paper, we have explored the optical characteristics, namely the shadow and the deflection angle, inherent to the solution of a 4D-AdS-Einstein–Gauss–Bonnet black hole. This solution, which finds its inspiration in noncommutative geometry, had previously been established in our previous work. The radius of the shadow was determined using the Hamilton-Jacobi method and the Carter separation. Our results revealed that the presence of noncommutativity in the background of spacetime impacts the variation of the shadow radius. More specifically, we have demonstrated that an increase in the parameter θ induces a decrease in the radius of the shadow. In a similar way, analogous observations have been made by studying the variation of the electric charge Q. The noncommutative parameter θ and the electric charge Q have been constrained regarding the EHT observation data of the M87* and Sgr A* black holes. Furthermore, the angle of deflection, which is the outcome of lensing by the black hole, has been derived following the Ishihara et al. approach for a receiver and source positioned at finite distances from the black hole in an asymptotically non-flat spacetime. The impact of the noncommutative parameter θ and the charge Q of the black hole are hence analyzed, and our results depict that these parameters have a significant influence on the angle at which light is deflected by the gravitational field of the black hole.