On M87$^*$ and SgrA$^*$ Observational Constraints of Dunkl Black Holes

In this work, we investigate the optical properties of a new black hole recently obtained from the Dunkl operator formalism involving a relevant parameter denoted by $\xi$. Concretely, we first investigate the shadows, the Lyapunov exponents of unstable nearly bound orbits and the spherically infalling accretion behaviors in terms of such a parameter. Then, we examine the effect of this parameter on the Dunkl black hole deflection angle in vacuum and medium backgrounds by manipulating the Gauss-Bonnet theorem. Exploiting the M87$^*$ and SgrA$^*$ optical bonds, we provide strong constraints on $\xi$ via the falsification mechanism.