The generalized virial theorem inf(R) gravity

Abstract

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