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arXiv · 2407.13262

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

Alberto Guilabert·Pelayo V. Calzada·Pedro Bargueño·Salvador Miret-Artés
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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 $f(R) = r_0^{-1}\left\lvert R-3/r_0^2\right\rvert^{1/2}$, where $r_0$ is a non-null constant. Finally, we briefly present some geometric properties of these solutions.

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Alberto Guilabert, Pelayo V. Calzada, Pedro Bargueño, Salvador Miret-Artés. 2024-07-18. Static and spherically symmetric vacuum spacetimes with non-expanding principal null directions in $f(R)$ gravity. https://doi.org/10.1140/epjc%2Fs10052-024-13063-3

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