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 general relativity, of the interior solutions.

• Received 26 July 2012

DOI:https://doi.org/10.1103/PhysRevD.86.104039