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

Abstract

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.

27 Pages, 15 Figures, 4 Tables

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