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

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arxiv 2007.13328 v1 pith:UPYE5FZC submitted 2020-07-27 gr-qc hep-th

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

classification gr-qc hep-th
keywords friedman-robertson-walkergeneralgravitypropertiessolutionstensorvacuumcondition
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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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