Generalized virial theorem in f(R) gravity

Understand

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.