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There should be two ways to describe the flat rotation curves of galaxies andcluster of galaxies. Either one can introduce a dark matter component for thematter filling the halo, or by modifying the gravity theory and give the flatrotation curve a geometrical nature. Here we adopt an f(R) model suitable fordescribing the effect. After matching the solution with the exterior solution,the effective density, radial and tangential pressures are obtained. Then theenergy conditions and lensing effect is investigated.

An f(R) model for dark matter: rotation curves and gravitational lensing