Test the Loop Quantum Gravity Theory via the Lensing Effect

Recently, scholars such as Lewandowski, Ma, and Yang have successfully derived a quantum-corrected black hole model in loop quantum gravity (Phys.Rev.Lett.130.101501 (2023)), which is a modification of the Schwarzschild black hole. In this paper, we calculate the strong/weak gravitational lensing effects under the quantum-corrected black hole model, taking the supermassive black holes M87* and SgrA* as the subjects of study to explore the impact of the quantum correction parameter α on the positions of images and the Einstein ring. Our calculations show that in the case of strong gravitational lensing, the lensing coefficient ā increases with an increase in the quantum correction parameter, while the deflection angle and the lensing coefficient b̄ decrease with an increase in the quantum correction parameter. The quantum correction parameter α has a significant impact in the context of supermassive black holes. In weak gravitational lensing, the quantum correction parameter α plays a suppressive role. Our theoretical analysis suggests that with advancements in future astrophysical observation techniques, it might be possible to test loop quantum gravity theory using the gravitational lensing effect.