Stellar Structure Equations in Extended Palatini Gravity

We consider static spherically symmetric stellar configurations in Palatini theories of gravity in which the Lagrangian is an unspecified function of the form $f(R,R_{\mu\nu}R^{\mu\nu})$. We obtain the Tolman-Oppenheimer-Volkov equations corresponding to this class of theories and show that they recover those of $f(R)$ theories and General Relativity in the appropriate limits. We show that the exterior vacuum solutions are of Schwarzschild-de Sitter type and comment on the possible expected modifications, as compared to GR, of the interior solutions.