Several $f(R)$ modified gravity models have been proposed which realize the correct cosmological evolution and satisfy solar system and laboratory tests. Although nonrelativistic stellar configurations can be constructed, we argue that relativistic stars cannot be present in such $f(R)$ theories. This problem appears due to the dynamics of the effective scalar degree of freedom in the strong gravity regime. Our claim thus raises doubts on the viability of $f(R)$ models.

• Received 22 July 2008

DOI:https://doi.org/10.1103/PhysRevD.78.064019