Circular orbits in modified gravity

A slight modification of the general relativistic metric under modified gravity is presented. The circular motion of massive particles is discussed in the new metric. It is shown that there are two roots at which circular motion can happen. However, while one root results in a stable circular orbit, the second represents a maxima which is very unstable because the attractive forces dominate as radius r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$r$\end{document} gets small and draw towards zero. Furthermore, we derive an equation for the orbital angular speed for the stable root in modified gravity and show that for large values of M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M$\end{document}, the modified orbital angular speed approaches the well known orbital angular speed. Finally, a description of photon orbits in the new metric is given and a derivation of the deflection angle is presented. Its shown that modified gravity can give a considerable contribution to the deflection angles of light rays.