Probing an Extended Uncertainty Principle black hole with gravitational lensings

We study signals of the weak and strong deflection gravitational lensings by an Extended Uncertainty Principle (EUP) black hole, which is based on a modified Heisenberg relation with an additional correction of position-uncertainty. Gravitational lensing observables, including positions, magnifications and differential time delays between lensed images, are obtained in both scenarios and analyzed for the supermassive black holes (SMBHs) in the Galactic Center (Sgr A*) and M87. We find that, for Sgr A*, measurements on the separation between the primary and secondary images in the weak deflection lensing and the apparent size of the photon sphere in the strong deflection lensing are two feasible ways to constrain EUP, imposing comparable lower bounds on the fundamental scale of EUP as similar to 10(10) m. For the SMBH in M87, measurements on strong deflection lensing observables are only available and they can give a much bigger lower bound as similar to 10(13) m. These results might provide hints for probing EUP black holes by gravitational lensings.