Black hole shadows in nonminimally coupled Weyl connection gravity

Abstract

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

and requiring consistency at the

$$2\sigma $$ 2 σ

level, we obtain

$$\omega \gtrsim 10^{11.7}M$$ ω ≳ 10 11.7 M

(model I),

$$\omega \gtrsim 10^{10.5}M$$ ω ≳ 10 10.5 M

(model II), and

$$\omega \sim 10^{12}M$$ 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.