Gravitational lensing by charged black hole in regularized $4D$ Einstein-Gauss-Bonnet gravity

Abstract: Among the higher curvature gravities, the most extensively studied theory is the so-called Einstein-Gauss-Bonnet (EGB) gravity, whose Lagrangian contains Einstein term with the GB combination of quadratic curvature terms, and the GB term yields nontrivial gravitational dynamics in $ D\geq5$. Recently there has been a surge of interest in regularizing, a $ D \to 4 $ limit of, the EGB gravity, and the resulting regularized $4D$ EGB gravity valid in $4D$. We consider gravitational lensing by Charged black holes in the $4D$ EGB gravity theory to calculate the light deflection coefficients in strong-field limits $\bar{a}$ and $\bar{b}$, while the former increases with increasing GB parameter $\alpha$ and charge $q$, later decrease. We also find a decrease in the deflection angle $\alpha_D$, angular position $\theta_{\infty}$ decreases more slowly and impact parameter for photon orbits $u_{m}$ more quickly, but angular separation $s$ increases more rapidly with $\alpha$ and charge $q$. We compare our results with those for analogous black holes in General Relativity (GR) and also the formalism is applied to discuss the astrophysical consequences in the case of the supermassive black holes Sgr A* and M87*.