Static and spherically symmetric vacuum spacetimes with non-expanding principal null directions in $f(R)$ gravity

Abstract

In this work we characterize all the static and spherically symmetric vacuum solutions in $f(R)$ gravity when the principal null directions of the Weyl tensor are non-expanding. In contrast to General Relativity, we show that the Nariai spacetime is not the only solution of this type when general $f(R)$ theories are considered. In particular, we find four different solutions for the non-constant Ricci scalar case, all of them corresponding to the same theory, given by $f(R)=r_0^{-1}{\left|R-3/r_0^2\right|}^{1/2}$, where $r_0$ is a non-null constant. Finally, we briefly present some geometric properties of these solutions.

arXiv comment7 pages, 4 figures, published in EPJC

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Cited by in corpus (1)

• Investigating the effects of gravitational lensing by Hu-Sawicki $\mathbf{f}(\mathbf{R})$ gravity black holes