Observable thin accretion disk around a self-dual black hole in loop quantum gravity

In this paper, we study a self-dual black hole (BH) in Loop Quantum Gravity (LQG), analyzing both timelike and null geodesics. Using observational data from Mercury's perihelion shift and the orbit of the S2 star around Sagittarius A$^{\star}$ (Sgr A$^{\star}$), we derive constraints on the polymeric function $P$. We further investigate photon trajectories near the self-dual BH under various scenarios to explore their observational relevance. Finally, we examine the properties of accretion disks around the self-dual BH in LQG, including their direct and secondary images, and study the redshift and the observed energy flux distribution across the accretion disk as measured by distant observers for different inclination angles. Our findings provide new insights into the physical nature and accretion properties of self-dual BHs in LQG and their possible observational consequences.