General properties of f (R) gravity vacuum solutions

摘要

General properties of vacuum solutions of f (R) gravity are obtained by the condition that the divergence of the Weyl tensor is zero and f '' not equal 0. Specifically, a theorem states that the gradient of the curvature scalar, del R, is an eigenvector of the Ricci tensor and, if it is timelike, the spacetime is a Generalized Friedman-Robertson-Walker metric; in dimension four, it is Friedman-Robertson-Walker.