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arXiv · 2007.13328

General properties of $\mathbf {f(R)}$ gravity vacuum solutions

Salvatore Capozziello·Carlo Alberto Mantica·Luca Guido Molinari
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Abstract

General properties of vacuum solutions of $f(R)$ gravity are obtained by the condition that the divergence of the Weyl tensor is zero and $f''\neq 0$. Specifically, a theorem states that the gradient of the curvature scalar, $\nabla R$, is an eigenvector of the Ricci tensor and, if it is time-like, the space-time is a Generalized Friedman-Robertson-Walker metric; in dimension four, it is Friedman-Robertson-Walker.

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Salvatore Capozziello, Carlo Alberto Mantica, Luca Guido Molinari. 2020-07-27. General properties of $\mathbf {f(R)}$ gravity vacuum solutions. https://doi.org/10.1142/s0218271820500893

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