Strong gravitational lensing in a Kerr black hole within Quantum Einstein Gravity

The detailed study of the strong gravitational lensing of a Kerr black hole within Quantum Einstein Gravity (QEG) is performed. We calculate the photon sphere, the deflection angle of light, and observables on the equatorial plane under the strong deflection limit in a vacuum. The presence of quantum effects reduces the radius of the photon sphere, the magnification, the position of relativistic images, and the time delays on the same side of the lens. However, it increases the strong deflection angle, the separations, and the time delays on the opposite side of the lens. By modeling M87* and Sgr A* as the Kerr black hole within QEG, we find that the time delays are more significant in M87*, while other observables are more pronounced in Sgr A*. Furthermore, we consider the influence of plasma on the gravitational lensing effect. Plasma causes an additional deflection of light, increasing the magnification, images position and the time delays, but decreasing the separations. More importantly, we calculate the time delays under the strong deflection limit in the presence of plasma, and they increase with higher plasma concentrations. Our research may help to evaluate the observational imprints left by such quantum effects in the propagation of light and the impact of plasma around black holes on gravitational lensing.