Gravitational lensing by black holes in the 4D Einstein-Gauss-Bonnet gravity

Recently, a non-trivial 4D Einstein-Gauss-Bonnet (EGB) theory of gravity, by rescaling the GB coupling parameter as α/(D−4), was formulated in [1], which bypasses Lovelock's theorem and avoids Ostrogradsky instability. The theory admits a static spherically symmetric black hole, unlike 5D EGB or general relativity counterpart, which can have both Cauchy and event horizons. We generalize previous work, on gravitational lensing by a Schwarzschild black hole, in the strong and weak deflection limits to the 4D EGB black holes to calculate the deflection coefficients ā and , while former increases and later decrease with increasing α. We also find that the deflection angle α_D, angular position θ_∞ and u_m decreases, but angular separation s increases with α. The effect of the GB coupling parameter α on positions and magnification of the source relativistic images is discussed in the context of SgrA* and M87* black holes. A brief description of the weak gravitational lensing using the Gauss-Bonnet theorem is presented.