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

Understand

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 $q$.