The interior spacetimes of stars in Palatini f(R) gravity
Abstract
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 δ F(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.
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