Strong gravitational lensing by Bardeen black holes in 4D EGB gravity: Constraints from supermassive black holes

Abstract

Observation indicates that many nearby galaxies host supermassive central black holes. We use the Bardeen black holes in four-dimensional Einstein–Gauss–Bonnet (4D EGB) gravity, with additional parameters-the coupling constant α̃ and charge q, as central black holes in various galaxies to investigate gravitational lensing properties in strong field regime. Taking the supermassive black holes Sgr A* and M87* as the lens, we compare observable signatures of 4D EGB Bardeen black holes with those of the Schwarzschild black holes. In the case of 4D EGB Bardeen black holes we observed that he angular position θ∞ for Sgr A* ∈ (23.19, 25.56) μ as, whereas for M87* it is ∈ ( 17.94,19.78) μ as. Further, the angular separation s, which is an increasing function of α̃ and q for Sgr A* and M87* differs significantly, respectively, in (0.032, 0.15) μ as and (0.025, 0.115) μ as. The deviations of the lensing observables Δθ∞ and Δs for 4D EGB Bardeen black hole (α̃=0.9,q=0.09) from the Schwarzschild black hole, respectively, can reach up to 2.38μ as and 0.12μ as for Sgr A* , 1.84μ as and 0.09μ as for M87*. On the other hand, the relative magnification ∈ (4.66,6.82). Considering twenty-one massive central black holes as lens, we also estimate the time delay ΔT2,1s between the first and second relativistic image to find that, e.g., the time delay for Sgr A* and M87*, respectively, can reach ∼9.86 min and ∼16023.93 min. We also show that the existing shadow size measurements place strong constraints on the parameters considered Bardeen model. This combination of gravitational lensing and EHT results may complement comprehensive restrictions on modifications of the general relativity.