(Non-) geodesic motion in chameleon Brans Dicke model

Based on \cite{16}, we assume there is a non-minimal coupling between the scalar field and matter in Brans-Dicke model. We analyzes the motion of different matter such as, massless scalar field, photon, massless perfect fluid (dust), massive perfect fluid and point particle matter in this theory. We show that the motion of massless scalar field and photon can satisfy null geodesic motion only in high frequency limit. Also we find that the motion of the dust and massive perfect fluid is geodesic for $L_m=-P$ and is non-geodesic for $L_m=\R$. Finally, we study the motion of point particle and show that the motion of this kind of matter is non-geodesic.

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