On Wormhole Throats in $f(R)$ Gravity Theory

Abstract

We study the existence and properties of wormhole throats in modified $f(R)$ gravity theory. Specifically, we concentrate on the cases where the lapse is not necessarily constant, and hence are not limited to the zero tidal force scenarios. In the class of theories whose actions are generated by Lagrangians of the form $f(R)=\sum {\alpha }_n{R}^n$ we find parameters which allow for the existence of energy condition respecting throats, which do not exist in Einstein gravity. We also consider the effect of the modified action on the anisotropy of the models, and find that modified gravity can minimize the amount of anisotropy required to support the existence of a throat. In both these respects, the sector containing theories with positive $n$ is more promising than the negative $n$ sector in comparison to Einstein gravity alone, with large $n$ being most favorable

36 pages, 35 figures. Updated version contains some stylistic improvements and added comments. Some typographical errors corrected. More references added. Matches version accepted for publication in Gen.Rel.Grav

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