Black hole shadows in nonminimally coupled Weyl connection gravity

We study black hole shadows in nonminimally coupled Weyl connection gravity, a metric-affine extension of general relativity in which spacetime is described by a metric and a Weyl vector field encoding non-metricity. Despite going beyond the Riemannian framework, the presence of a non-dynamical Weyl vector ensures second-order field equations. The theory admits Schwarzschild- and Reissner–Nordström-like solutions modified by a Weyl integration constant that parametrizes deviations from General Relativity. By computing the corresponding shadow radii and confronting them with the Event Horizon Telescope constraints on Sgr A*, we place observational bounds on the Weyl parameter. Assuming an observer distance rO = 4.1× 10¹⁰M r O = 4.1 × 10 10 M and requiring consistency at the 2σ 2 σ level, we obtain ω 1011.7M ω ≳ 10 11.7 M (model I), ω 1010.5M ω ≳ 10 10.5 M (model II), and ω ~ 10¹²M ω ∼ 10 12 M (model III). Our results show that present horizon-scale imaging already sets meaningful limits on spacetime non-metricity. This work highlights the power of black hole shadow observations as probes of extended gravitational dynamics and establishes a direct link between Weyl-based theories and current astrophysical data.