The generalized virial theorem inf(R) gravity

We generalize the virial theorem in f(R) modified gravity using the collisionless Boltzmann equation. We find supplementary geometric terms in the modified Einstein equation providing an effective contribution to the gravitational energy. The total virial mass is proportional to the effective mass associated with the new geometrical term, which may account for the well-known virial theorem mass discrepancy in clusters of galaxies. The model predicts that the geometric mass and its effects extend beyond the virial radius of the clusters. We also consider the behavior of the galaxy cluster velocity dispersion in f(R) models. The metric inside the galactic cluster, as well as the Lagrangian of the modified gravity model, are obtained in terms of quantities directly related to the physical properties of the clusters, and which can be determined from astrophysical observations. Thus, the f(R) virial theorem can be an efficient tool in observationally testing the viability of this class of generalized gravity models. © IOP Publishing Ltd.