Observational signatures of quantum-corrected RN blackhole

TL;DR

This work investigates observational signatures of a quantum-corrected Reissner–Nordström black hole by introducing a dimensionless ratio $\Pi = a/Q$ to quantify competition between repulsive quantum corrections and classical charge. Using the Wu–Liu metric, it derives how the parameter $a$ shifts horizon and photon-sphere locations, and derives a shadow radius approximation $R_{sh} \approx 3\sqrt{3}M\left(1 - \frac{Q^2}{18M^2} + \frac{Q^2\Pi}{36M^2}\right)$, illustrating the competing effects on shadow size. The strong-deflection angle is computed via Bozza–Tsukamoto formalism, showing that $\Pi$ expands the photon sphere and reduces deflection relative to charge-enhanced cases, with key coefficients depending on the metric derivatives at the photon sphere. Confronting these predictions with EHT constraints for Sgr A* and M87* yields a robust bound $0 \le \Pi \lesssim 0.7$, indicating quantum geometric corrections cannot exceed about 70% of the black hole charge; the study demonstrates strong-field lensing as a viable phenomenological probe of Planck-scale physics in astrophysical black holes.

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 $Π= \mathrm{a}/Q$. We find that consistency with the shadow angular diameter of Sgr A* requires $0 \le Π\lesssim 0.7$, 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.

Figures (3)

• Figure 1: The variation of the shadow radius with electric charge $Q$ for the M87* black hole (above) and Sgr. A* (below). The dashed lines indicate EHT observational bounds.
• Figure 2: The variation of the shadow radius with quantum parameter $\Pi$ for the M87* black hole (above) and Sgr. A* (below). The dashed lines indicate EHT observational bounds.
• Figure 3: The behavior of the strong deflection angle $\alpha(r_0)$ as a function of the closest approach distance $r_0$ for M87* (top) and Sgr A* (bottom). The vertical asymptotes indicate the location of the photon sphere for varying values of $\Pi$. The shift in these asymptotes corresponds to the variation in shadow size constrained by EHT observations.