First order formalism of \(f(R)\) gravity
The authors analyze a general class of geometrical theories of gravitation with a matter free Lagrangian of the form \({\mathcal L}=\sqrt{- g}\) \(f(R)\), where \(f\) is an arbitrary function of the curvature scalar \(R\). They assume arbitrary connection coefficients and vary the action considering the connections and the metric as independent fields. The resulting theory is a subclass of conformally metric theories of the Weyl type. It is found that except for the special case of general relativity, i.e. \(f(R)=R\) the strong equivalence principle is not true. The general theory has a weak field, small velocity limit that coincides with the Newtonian limit only if \(f''(0)=0\). If this last condition is not fulfilled, the deviation for the Newtonian value of the acceleration of a test body is proportional to the gradient of the mass density. The authors believe that such effects may be significant in the interior of a stellar system when thermodynamic configurations are rapidly changing.
conformally metric theories of the Weyl type
scientific article; zbMATH DE number 205364