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 alpha/(D-4), was formulated in [10], 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 (a) over bar and (b) over bar, while former increases and later decrease with increasing alpha. We also find that the deflection angle alpha(D), angular position theta(infinity) and u(m) decreases, but angular separation s increases with alpha. The effect of the GB coupling parameter alpha 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.