标题： 关于$f(R)$引力中的引力波的能量-动量张量 显示英文标题

标题： On energy-momentum tensor for gravitational waves in $f(R)$ gravity

摘要： 经典Isaacson方法描述高频引力波平均能动张量的反作用，被推广到$f(R)$引力情形。 从一开始便假设初始背景可以是任意的。 接下来将其限制到de Sitter空间，这是$f(R)$引力背景下反作用研究的一个新方面。 将de Sitter空间视为背景时空，使我们能够完全实现平均化过程。 利用关于de Sitter空间的结果，并推广Isaacson方法，我们在额外弯曲（平均化）的背景上构建了平均能动张量。 给出了保持de Sitter图像的参数关系以及破坏该图像的参数关系。 我们的结果推广了之前使用平坦（闵可夫斯基）时空作为初始背景的研究者们在$f(R)$引力中的结果。 显示英文摘要

摘要： The classical Isaacson's procedure for describing back-reaction of the averaged energy-momentum for high frequency gravitational waves is generalized to $f(R)$ gravity case. From the beginning it is assumed that an initial background could be arbitrary one. By next steps it is restricted to de Sitter space that is a novelty for the study of a back-reaction in $f(R)$ gravity. Consideration of the de Sitter space as a background spacetime allows us to provide the averaging procedure completely. Using the results on the de Sitter space and generalizing the Isaacson procedure, we construct the averaged energy-momentum on an additionally curved (averaged) background. Relations of parameters, which preserve the de Sitter picture, and which disturb it are given. Our results generalize results of previous authors who use flat (Minkowski) spacetime as the beginning background in $f(R)$ gravity.