Shadows and parameter estimation of rotating quantum corrected black holes and constraints from EHT observation of M87* and Sgr A*

The scarcity of quantum gravity (QG) inspired rotating black holes limits the progress of testing QG through Event Horizon Telescope (EHT) observations. The EHT imaged the supermassive black holes, Sgr A* and M87*, revealing an angular shadow diameter of $d_{sh}=48.7\pm 7\mu$as with a black hole mass of $M=4.0_{-0.6}^{+1.1}\times {10}^{6}M\odot$ for Sgr A*. For M87*, with a mass of $M=(6.5\pm 0.7)\times {10}^9{M}_{\odot }$, the EHT measured an angular diameter of ${\theta }_d=42\pm 3\mu$as. We present rotating quantum-corrected black hole (RQCBH) spacetimes with an additional QC parameter $\alpha$ and constrain it by EHT observations. For angular shadow diameter ($d_{sh}$) of Sgr A* at ${\theta }_o={50}^0$, the bounds are $0.0\le \alpha \le 1.443M^2$ and $a\in (0,0.8066M)$. For ${\theta }_o={90}^0$, the bounds are $0.0\le \alpha \le 1.447M^2$ and $a\in (0,0.894M)$. While for M87* at inclination ${\theta }_o={17}^0$, the bounds are $a\in (0,0.8511M)$ at $\alpha =0$ and $a\in (0,0.6157M)$ at $\alpha =0.8985M^2$. For ${\theta }_o={90}^0$, the bounds are $a\in (0,0.8262M)$ at $\alpha =0$ and $a\in (0,0.9799M)$ at $\alpha =0.4141M^2$. These results show that $\alpha$ significantly affects the shadows, offering key constraints on QG models. With EHT constraints from Sgr A and M87*, RQCBHs and Kerr black holes are indistinguishable in much of the EHT-constrained parameter space, making RQCBHs strong candidates for astrophysical black holes along with other BHs, e.g., regular black holes and other quantum-corrected solutions.