Effects of geometric optics in conformal Weyl gravity

We have investigated effect of geometric optics as the rotation of polarization vector of light in spacetime of gravitational compact object in the fourth-order theory of conformal Weyl gravity. The Pineault–Roeder method is applied to the rotating Weyl metric, and analytical results are obtained in the limit of weak field and or slow rotation. For the photon traveling parallel to the symmetry axes from the equatorial plane to infinity, the rotation of the polarization plane depends on the Weyl parameter γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document} on the contrary to the Kerr spacetime where there is no rotation of polarization plane for this case.