Polarized Equatorial Emission around Kerr Black Holes with Synchronized Scalar Hair. I. Direct images

We investigate the polarization properties of the direct images of a geometrically and optically thin accretion disk around fully self-consistent models of rotating Kerr black holes with synchronized bosonic hair. The presence of a massive scalar field alters the geodesic structure of the spacetime and thus leaves an imprint on the polarization of radiation emitted near the black hole horizon. To study this effect, we employ a simple analytical model of a geometrically thin accretion disk, orbiting in the equatorial plane and emitting synchrotron radiation. The main deviation from a corresponding Kerr black hole in general relativity is found to be a dephasing in the twist of the polarization vector, which is surprisingly larger for the least scalarized solutions we consider. This behavior suggests that polarization observables are primarily sensitive to local geometric and transport effects along photon trajectories rather than to the overall scalar field strength. Furthermore, our results demonstrate that while equatorial magnetic fields produce qualitatively similar polarization patterns to Kerr black holes in general relativity, vertical magnetic fields at high observer inclinations can lead to a characteristic reversal of the twist direction of the polarization vector.