Accretion disks and photon trajectories around black holes in modified gravity

This paper investigates the properties of accretion disks around black holes within the frameworks of metric-affine gravity and Starobinsky–Bel–Robinson gravity, using the Novikov–Thorne model. By incorporating modifications to spacetime geometry introduced by these alternative gravity theories, we analyze the impact of key parameters such as the coupling constants [Formula: see text] in Starobinsky–Bel–Robinson gravity and [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] in metric-affine gravity on the structure, lensing effects, and observational appearance of accretion disks. The Novikov–Thorne model provides a robust framework for studying thin accretion disks in strong gravitational fields, allowing for detailed examination of photon trajectories and gravitational lensing. Our results reveal that the dimensionless coupling parameters in these gravity theories significantly alter the curvature of spacetime, resulting in observable distortions of the accretion disk. In metric-affine gravity, the spin charge dominates the distortion of the accretion disk, while shear and dilation charges introduce subtler effects. In Starobinsky–Bel–Robinson gravity, increasing [Formula: see text] enhances gravitational lensing, causing a transition from circular to hat-like elliptical disk shapes. We also analyze that observation angle and radial distances also play a crucial role in gravitational lensing.