Optical appearance of black holes surrounded by dust fields in <i>f</i> ( <i>R</i> , <i>T</i> ) gravity by a thin accretion disk

We investigate whether matter-geometry couplings in [Formula: see text] gravity generate observable deviations in black hole (BH) imaging that cannot be reproduced by environmental effects alone. For this purpose, we analyze the formation and observational signatures of light phenomena such as BH shadow formation, optical properties, and luminosity variations in BHs surrounded by dust fields (BHDF) within [Formula: see text] gravity, illuminated by a thin-disk accretion flow. To analyze the impact parameter ([Formula: see text]) regions, we apply the ray tracing method for lensed, direct, and photon ring emissions. Subsequently, by using a transfer function technique supported by a geodesic study, we derive the total observed intensity and flux variations to identify how the radiation from different parts of the accretion disk changes the BH’s observable characteristics. This gives us the ability to determine how BHs visually look when lit by three widely used frameworks of optically and geometrically thin accretion disks in a direct, facing position. Our study shows that alterations in the coupling constraints [Formula: see text] and [Formula: see text] have a major impact on both the intensity pattern and the shadow outline. In particular, an increase in [Formula: see text] yields a dramatic reduction in the emission area, observed intensity, and shadow size, whereas changes in [Formula: see text] bring about a more gradual decrease. The results indicate that BH imaging features are extremely sensitive to the impacts of changed gravity as well as the matter environment distribution. Besides that, adding dust fields in [Formula: see text] gravity provides a diagnostic tool for tweaked gravity theories and will be valuable for future research.