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 $$r_O = 4.1\times 10^{10}M$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>r</mml:mi> <mml:mi>O</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>4.1</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>10</mml:mn> </mml:msup> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> and requiring consistency at the $$2\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>σ</mml:mi> </mml:mrow> </mml:math> level, we obtain $$\omega \gtrsim 10^{11.7}M$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ω</mml:mi> <mml:mo>≳</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mn>11.7</mml:mn> </mml:mrow> </mml:msup> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> (model I), $$\omega \gtrsim 10^{10.5}M$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ω</mml:mi> <mml:mo>≳</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mn>10.5</mml:mn> </mml:mrow> </mml:msup> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> (model II), and $$\omega \sim 10^{12}M$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ω</mml:mi> <mml:mo>∼</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>12</mml:mn> </mml:msup> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> (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.