Static Spherically Symmetric Solutions in Extended Palatini Gravity

TL;DR

This paper derives and analyzes static spherically symmetric solutions in extended Palatini gravity theories, generalizing known results from f(R) gravity and General Relativity, and discusses potential modifications to stellar structures.

Contribution

It formulates the Tolman-Oppenheimer-Volkoff equations for a broad class of Palatini theories involving R and R_{ u u}R^{ u u}, extending previous models.

Findings

Recovered TOV equations reduce to GR and f(R) limits.

Derived exterior vacuum solutions for these theories.

Discussed potential modifications to stellar interior solutions.

Abstract

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 compute exterior vacuum solutions and comment on the possible expected modifications, as compared to GR, of the interior solutions.