The 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 neglible in models for which $\delta F(R) \equiv \partial f/\partial R - 1$ is a decreasing function of R however. As a result, both Solar System constraints and stellar dynamics are perfectly consistent with $f(R) = R - \mu^4/R$.