Testing Rotating Regular Metrics with EHT Results of Sgr A*

Abstract: The Event Horizon Telescope (EHT) observation unveiled the first image of supermassive black hole Sgr A* showing a shadow of diameter $\theta_{sh}= 48.7 \pm 7\,\mu$as with fractional deviation from the Schwarzschild black hole shadow diameter $\delta = -0.08^{+0.09}{-0.09}~\text{(VLTI)},-0.04^{+0.09}{-0.10}~\text{(Keck)}$. The Sgr A* shadow size is within $~10\%$ of the Kerr predictions, providing us with another tool to investigate the nature of strong-field gravity. We use the Sgr A* shadow observables to constrain metrics of four independent and well-motivated, parametrically different from Kerr spacetime, rotating regular spacetimes, and the corresponding no-horizon spacetimes. We present constraints on the deviation parameter $g$ of rotating regular black holes. The shadow angular diameter $\theta_{sh}$ within $1 \sigma$ region, places bounds on the parameters $a$ and $g$. Together with EHT bounds on $\theta_{sh}$ and $\delta$ of Sgr A*, our analysis concludes that the three rotating regular black holes, viz., Bardeen Hayward, and Simpson-Visser black holes, and corresponding no-horizon spacetimes agree with the EHT results of Sgr A*. Thus, these three rotating regular spacetimes and Kerr black holes are indiscernible in some parameter space, and one can not rule out the possibility of the former being strong candidates for astrophysical black holes.