In this paper, we study, in the Newtonian limit, the virial theorem in the context of a scalar tensor fourth order gravity. In particular, we show, that for a isolated galaxy in viral equilibrium, a specific class of scalar tensor fourth order gravity, i.e. \(f(R,\phi )+\omega (\phi )\,\phi _{;\alpha }\,\phi ^{;\alpha }\) in not suitable to explain the large fraction of dark matter necessary to have the flatness of the galaxies rotation curves experimentally observed.

中文翻译：

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标量张量四阶引力中的维里定理

在本文中，我们在牛顿极限中研究了标量张量四阶引力背景下的维里定理。特别是，我们表明，对于病毒平衡中的孤立星系，特定类别的标量张量四阶引力，即\(f(R,\phi )+\omega (\phi )\,\phi _{;\ alpha }\,\phi ^{;\alpha }\)不适用于解释实验观察到的星系旋转曲线平坦所需的大部分暗物质。