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 $0.0 \leq \alpha \leq 1.443 M^2$ and $a \in (0, 0.8066 M)$. For $\theta_o = 90^0$, the bounds are $0.0 \leq \alpha \leq 1.447 M^2$ and $a \in (0, 0.894 M)$. While for M87* at inclination $\theta_o = 17^0$, the bounds are $a \in (0, 0.8511 M)$ at $\alpha=0$ and $a \in (0, 0.6157 M)$ at $\alpha=0.8985 M^2$. For $\theta_o = 90^0$, the bounds are $a \in (0, 0.8262 M)$ at $\alpha=0$ and $a \in (0, 0.9799 M)$ at $\alpha=0.4141 M^2$. 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.