标题： 平均化爱因斯坦方程：线性化情况 显示英文标题

标题： Averaging Einstein's Equations: The Linearized Case

摘要： 我们引入了一种简单直接的平均过程，这是在电动力学中常用的一种方法的推广，并表明它具有广义相对论和宇宙学中线性化平均所需的所有特性——对于弱场和扰动FLRW情况。 特别是我们证明了它在这些情况下产生近似张量量，并且将其应用于精确的FLRW度规时，在局部坐标积分的一阶近似下，会得到另一个FLRW度规。 最后，我们指出了任何线性化平均过程在处理由大振幅小尺度和中等尺度不均匀性平均所得的宇宙学扰动时的重要限制，并表明在这些情况下，我们的平均过程可以近似通过Zotov和Stoeger的方法来实现。 显示英文摘要

摘要： We introduce a simple and straight-forward averaging procedure, which is a generalization of one which is commonly used in electrodynamics, and show that it possesses all the characteristics we require for linearized averaging in general relativity and cosmology -- for weak-field and perturbed FLRW situations. In particular we demonstrate that it yields quantities which are approximately tensorial in these situations, and that its application to an exact FLRW metric yields another FLRW metric, to first-order in integrals over the local coordinates. Finally, we indicate some important limits of any linearized averaging procedure with respect to cosmological perturbations which are the result of averages over large amplitude small and intermediate scale inhomogeneities, and show our averaging procedure can be approximately implemented by that of Zotov and Stoeger in these cases.