An Upper Limit on the Charge of the Black Hole Sgr A* from EHT Observations

The Event Horizon Telescope (EHT) recently released an image of the supermassive black hole Sgr A* showing an angular shadow diameter $d_{sh}= 48.7 \pm 7\,\mu$as and Schwarzschild shadow deviation $\delta = -0.08^{+0.09}_{-0.09}~\text{(VLTI)},-0.04^{+0.09}_{-0.10}~\text{(Keck)}$ using a black hole mass $M = 4.0^{+1.1}_{-0.6} \times 10^6 M_\odot $. The EHT image of Sgr A* is consistent with a Kerr black hole's expected appearance, and the results directly prove the existence of a supermassive black hole at the center of the Milky Way. Here, we use the EHT observational results for Sgr A* to investigate the constraints on its charge with the aid of Kerr-like black holes, paying attention to three leading rotating models, namely Kerr--Newman, Horndeski, and hairy black holes. Modeling the supermassive black hole Sgr A* as these Kerr-like black holes, we observe that the EHT results of Sgr A* place more strict upper limits on the parameter space of Kerr--Newman and Horndeski black holes than those placed by the EHT results for M87*. A systematic bias analysis reveals that, observational results of future EHT experiments place more precise limits on the charge of black hole Sgr A*. Thus, the Kerr-like black holes and Kerr black holes are indiscernible in a substantial region of the EHT-constrained parameter space; the claim is substantiated by our bias analysis.