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 $r_O = 4.1\times 10^{10}M$ and requiring consistency at the $2σ$ level, we obtain $ω\gtrsim 10^{11.7}M$ (model I), $ω\gtrsim 10^{10.5}M$ (model II), and $ω\sim 10^{12}M$ (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.

Figures (5)

• Figure 1: Shadow radius $r_{sh}$ of model I \ref{['eq:model_I']} as a function of the Weyl constant $\omega$ (black line), for an observer at a distance of $r_O = 4.1\times 10^{10}M$. The shaded areas represent the confidence intervals of Sgr A*'s shadow radius at 1$\sigma$ (dark gray) and at 2$\sigma$ (light gray).
• Figure 2: Shadow radius $r_{sh}$ of model II \ref{['eq:model_II']} as a function of the Weyl constant $\omega$ (black line), for an external observer at $r_O = 4.1\times 10^{10}M$. The shaded areas represent the confidence intervals of Sgr A*'s shadow radius at 1$\sigma$ (dark gray) and at 2$\sigma$ (light gray).
• Figure 3: Shadow radius $r_{sh}$ of model III \ref{['eq:model_III']} as a function of the Weyl constant $\omega$, for three dressed charge values: $\tilde{Q}=0$ (black solid line), $\tilde{Q}=0.4M$ (gold dashed line), $\tilde{Q}=0.8 M$ (dotted blue line); considering an external observer at $r_O = 4.1\times 10^{10}M$. The shaded areas represent the confidence intervals of Sgr A*'s shadow radius at 1$\sigma$ (dark gray) and at 2$\sigma$ (light gray).
• Figure 4: Shadow radius $r_{sh}$ of model III \ref{['eq:model_III']} as a function of the correction factor $\zeta$, for three charge values: $Q=0$ (black solid line), $Q=0.4M$ (gold dashed line), $Q=0.8 M$ (dotted blue line); considering an external observer at $r_O = 4.1\times 10^{10}M$. The shaded areas represent the confidence intervals of Sgr A*'s shadow radius at 1$\sigma$ (dark gray) and at 2$\sigma$ (light gray).
• Figure 5: Visual appearance, in the impact parameter space, of the spacetime geometry modeled by equation \ref{['eq:model_III_flat']}. The images are organized according to the emission profile: GLM3 (top line), GLM1 (middle line) and GLM2 (bottom line); and the value of the correction factor: $\zeta=0.94$ (left column), $\zeta=1.00$ (middle column) and $\zeta=1.175$ (right column). We consider a Weyl black hole with a charge $Q = 0.94 M$, as seen at a face-on orientation, by an observer located at a distance of $r_O = 4.1\times 10^{10}M$.