Probing the one-loop quantum correction on the Schwarzschild black hole with the gravitational lensing images of a point-like source

Abstract

The one-loop quantum corrections of General Relativity contribute to understand its ultraviolet completion and can be tested by directly imaging the supermassive black hole in our Galactic center. In this work, we analytically investigate the weak deflection gravitational lensing of the one-loop quantum corrected Schwarzschild spacetime that is characterized by a normalized quantum correction parameter \(\lambda \), and discuss the detectability of its weak deflection lensing observables. We find that these observables have the potential to be measured but their deviations from those of a Schwarzschild black hole can not be distinguished due to current limited resolution. To gain deeper insights into the quantum nature, we further study the strong deflection gravitational lensing analytically. According to the shadow measurement of Sgr A* by the Event Horizon Telescope, we obtain a constraint on \(\lambda \) and demonstrate that the strong deflection lensing observables such as the angular separation, brightness difference and time delay of the relativistic images are beyond the reach of present capacity in this allowable range. Consequently, identifying the quantum effects around such a corrected Schwarzschild spacetime with gravitational lensing is not feasible at current stage.