Tests of Loop Quantum Gravity from the Event Horizon Telescope Results of Sgr A${}^{\ast }$

Abstract

The Event Horizon Telescope (EHT) collaboration's image of the compact object at the galactic center is the first direct evidence of the supermassive black hole (BH) Sgr A${}^{\ast }$. The shadow of Sgr A${}^{\ast }$ has an angular diameter $d_{sh}=48.7\pm 7\mu$as with fractional deviation from the Schwarzschild BH shadow diameter $\delta =-0.08_{-0.09}^{+0.09},-0.04_{-0.10}^{+0.09}$ (for the VLTI and Keck mass-to-distance ratios). Sgr A${}^{\ast }$'s shadow size is within $10\%$ of Kerr predictions, equipping us with yet another tool to analyze gravity in the strong-field regime, including testing loop quantum gravity (LQG). We use Sgr A${}^{\ast }$'s shadow to constrain the metrics of two well-motivated LQG-inspired rotating BH (LIRBH) models characterized by an additional deviation parameter $L_q$, which recover the Kerr spacetime in the absence of quantum effects ($L_q\to 0$). When increasing the quantum effects through $L_q$, the shadow size increases monotonically, while the shape gets more distorted, allowing us to constrain the fundamental parameter $L_q$. We use the astrophysical observables shadow area $A$ and oblateness $D$ to estimate the BH parameters. It may be useful in extracting additional information about LIRBHs. While the EHT observational results completely rule out the wormhole region in the LIRBH-2, a substantial parameter region of the generic BHs in both models agrees with the EHT results. We find that the upper bounds on $L_q$ obtained from the shadow of Sgr A${}^{\ast }$ -- $L_q\lesssim 0.0423$ and $L_q\lesssim 0.0821$ for the two LIRBHs, respectively -- are more stringent than those obtained from the EHT image of M87${}^{\ast }$.

15 pages, 6 figures, 2 tables. Matched to the published version

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