Observational signatures of quantum-corrected RN blackhole

Abstract

We investigate the observational signatures of a quantum-corrected Reissner-Nordstr\"om (RN) black hole to constrain Planck-scale modifications to spacetime geometry using current astrophysical data. By analyzing the null geodesic structure, we demonstrate that the quantum correction parameter, $\mathrm{a}$, acts as a repulsive geometric potential that opposes the gravitational compactification induced by the electric charge, $Q$. This competition leads to a parameter degeneracy wherein a highly charged, quantum-corrected black hole can mimic the shadow size of a classical Schwarzschild black hole. To resolve this, we employ the strong-field limit formalism to derive the deflection angle and the observables associated with relativistic Einstein rings. Our analysis reveals that while the electric charge enhances the deflection angle, the quantum correction suppresses it, providing a theoretical mechanism to distinguish the two effects. Confronting these predictions with the latest Event Horizon Telescope (EHT) observations, we derive robust constraints on the dimensionless parameter $\Pi = \mathrm{a}/Q$. We find that consistency with the shadow angular diameter of Sgr. A$^*$ requires $0 \le \Pi \lesssim 0.7$, implying that quantum geometric corrections cannot exceed approximately $70\%$ of the black hole charge without violating empirical bounds. These results highlight the potential of strong-field lensing to place precise phenomenological limits on quantum gravity candidates.