Shadows of Kerr-like black holes in $4D$ Einstein-Gauss-Bonnet gravity and constraints from EHT observations

The M87* black hole shadow observation by the Event Horizon Telescope (EHT) has enabled us to test the modified gravity theories in the extreme-field regime and estimating the black hole parameters. Having this assertion, we investigate the Kerr-like rotating black holes in $4D$ Einstein-Gauss-Bonnet (EGB) gravity and deduce their shadows. Considering the inclination angle $\theta_0=17^o$, we show that the EGB black hole shadows are smaller and more distorted than for the Kerr black holes. Modelling the M87* black hole as the EGB black hole, we predict the shadow angular size $35.7888\mu as\leq \theta_d\leq 39.6192\mu as$. The M87* black hole shadow angular size $\theta_d=42\pm 3\mu as$, within the 1$\sigma$ region, constrains the GB coupling parameter and the black hole spin parameter. Interestingly, the circularity deviation of the EGB black hole shadows is smaller than the bounded deduced for the M87* black hole.