Shadows of naked singularity in Brans–Dicke gravity

Abstract We investigate exact vacuum solutions in Brans–Dicke (BD) gravity, focusing on their implications for black hole shadow imaging. Motivated by the Event Horizon Telescope (EHT) observations, we revisit a class of BD solutions that exhibit a naked singularity. These solutions, despite lacking a conventional event horizon, exhibit photon spheres and produce shadow-like features. We analyze null geodesics and perform ray-tracing simulations under an optically thin accretion disk model to generate synthetic images. Our results show that BD naked singularities can cast shadows smaller than those of Schwarzschild black holes of equivalent mass. This requires, however, negative values for the BD parameter $$\omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ω</mml:mi> </mml:math> (in the range $$-3/2&lt; \omega &lt; 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> <mml:mo>&lt;</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> ). The lower bound on $$\omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ω</mml:mi> </mml:math> is compatible with the absence of ghosts. Although such $$\omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ω</mml:mi> </mml:math> range is outside the Solar System bounds, our results are relevant for a larger class of modified gravity models whose local behaviour can be approximated by Brans–Dicke gravity. These findings suggest that BD naked singularities are possible candidates for compact astrophysical objects.