General properties of f(R) gravity vacuum solutions

General properties of vacuum solutions of () gravity are obtained by the condition that the divergence of the Weyl tensor is zero and ′′≠0. Specifically, a theorem states that the gradient of the curvature scalar, ∇, 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.