Strong Gravitational Lensing by Rotating Quantum-Corrected Black Holes: Insights and Constraints from EHT Observations of M87* and Sgr A*

We study gravitational lensing in the strong-field limit using the rotating quantum-corrected black hole (RQCBH) with an additional parameter $\alpha$ besides mass $M$ and spin parameter $a$. We discover a decrease in the deflection angle $\alpha_D$, the photon sphere radius $x_{ps}$, and the angular position $\theta_{\infty}$. The flux ratio of the first image to all subsequent images, $r_{mag}$, decreases rapidly as $\alpha$ increases. We compare RQCBH observables with those of Kerr black holes, using Sgr A* and M87* as lenses to observe the effect of the quantum-corrected parameter $\alpha$. For Sgr A*, the angular position $\theta_\infty$ in $\in~(14.8-26.3)~\mu as$, while for M87* $\in~(11.12-19.78)~\mu as$. The angular separation $s$, for supermassive black holes (SMBHs) SgrA* and M87*, differs significantly, with values ranging $\in~(0.033-0.79)~\mu as$ for Sgr A* and $\in~(0.033-0.59)~\mu as$ for M87*. The deviations of the lensing observables $|\Delta\theta_\infty|$ and $|\Delta s|$ for RQCBH ($a=0.8,\alpha=0.4$) from Kerr black holes can reach up to $1.6~\mu as$ and $0.41~\mu as$ for Sgr A*, and $1.2~\mu as$ and $0.31~\mu as$ for M87*. The relative magnitude $r_{mag}$ $\in~(1.81-6.82)~\mu as$. We also compared the time delays between the relativistic images in the 22 SMBHs at the center of various galaxies. We found that RQCBH can be quantitatively distinguished from Kerr black holes. Interestingly, the time delay for Sgr A* and M87* can reach approximately 24.95 min and 308.15 hrs, respectively. Our analysis concludes that, within the 1$\sigma$ region, a significant portion of the parameter space agrees with the EHT results of M87* and Sgr A*.