Rotating charged black hole in $4D$ Einstein-Gauss-Bonnet gravity: Photon motion and its shadow

Abstract: We construct a charged rotating black hole in 4D Einstein-Gauss-Bonnet (EGB) gravity starting from charged black hole in 4D EGB gravity using complex coordinate transformations suggested by Newman-Janis. Further, we have studied the null geodesics to investigate the shape of the shadow cast by a rotating charged black hole in 4D EGB gravity. Also we have discussed their horizon properties and shadow cast. The phenomenon of black hole shadows alongwith the horizon structure and energy emission has been analysed to see the influence of Gauss-Bonnet term and black hole charge on horizon, shadow, effective potential and energy emission rate which are compared to their non rotating counterpart. It has been seen that the Gauss Bonnet parameter have an influence on the shape and size of the shadow as well as on the effective potential, horizon and energy emission rate.