Probing black hole in metric-affine gravity through thermodynamics, shadows, and accretion disks

In this work, we explore the optical, dynamical, and thermodynamical properties of black holes in the framework of metric-affine gravity, a geometric extension of general relativity that naturally incorporates torsion and nonmetricity. Motivated by the need to probe quantum gravity effects and observational deviations from Einstein’s theory, we investigate how Lagrangian parameters ([Formula: see text], [Formula: see text]) and gravitational charges ([Formula: see text], [Formula: see text], [Formula: see text]) influence black hole thermodynamics, shadows, and observed intensities. We introduce quantum gravity-inspired corrections via Barrow entropy and logarithmic entropy terms to study their effect on black hole phase transitions and stability. Our findings reveal that increasing the Barrow parameter [Formula: see text] and correction parameter [Formula: see text] leads to rich thermal behavior, including multiple stability regions and critical points not present in classical black holes. The heat capacity and Gibbs free energy demonstrate second- and first-order phase transitions, respectively, offering thermodynamic signatures of underlying spacetime fractality. In the optical domain, we analyze the structure of the effective potential, shadow silhouettes, and intensity distributions from static spherical accretion. We show that increasing [Formula: see text] amplifies gravitational lensing and redshift effects, enlarges the shadow size, and suppresses observed luminosity. Furthermore, spin, dilation, and shear charges influence photon trajectories and intensity profiles, providing potential observational tools to distinguish MAG black holes from their GR counterparts.