Interior spacetimes of stars in Palatini f(R) gravity

We study the interior spacetimes of stars in the Palatini formalism of f(R) gravity and derive a generalized Tolman-Oppenheimer-Volkoff and mass equation for a static, spherically symmetric star. We show that matching the interior solution with the exterior Schwarzschild-de Sitter solution in general gives a relation between the gravitational mass and the density profile of a star, which is different from the one in general relativity. These modifications become negligible in models for which δF(R)≡∂f/∂R-1 is a decreasing function of R however. As a result, both Solar System constraints and stellar dynamics are perfectly consistent with f(R)=R-μ4/R