Observational signatures of strong gravitational lensing in GUP-modified Schwarzschild black holes

We investigate gravitational lensing in strong-field limit by a static spherically symmetric GUP-modified Schwarzschild black holes having additional parameter epsilon. We found that influences of negative and positive values of epsilon parameter differ from Schwarzschild black hole. We expand the deflection angle of the photon in the neighborhood of complete capture, defining a strong field limit in opposition to the standard weak field limit. This expansion is performed fora generic spherically symmetric spacetime without referencing the field equations and assuming that the light ray follows the geodesics equation. We prove that the deflection angle always diverges logarithmically when the minimum impact parameter is reached. We apply this general formalism to Schwarzschild GUP black holes. We then compare the coefficients characterizing these metrics and find that different strong field limits characterize different collapsed objects. The strong field limits coefficients, such as the relativistic images' position and magnification, are directly connected to the observables. As a concrete example, we consider the black hole at the center of our galaxy and estimate the optical resolution needed to investigate its strong field behavior through its relativistic images.