标题： 在LTB尘埃模型中的平均和精确扰动 显示英文标题

标题： Averaging and exact perturbations in LTB dust models

摘要： 我们引入了一个标量加权平均("q-平均")，作用于球对称Lemaitre-Tolman-Bondi (LTB)尘埃模型中的同心共动区域。 该平均形式允许对模型进行优雅的坐标无关的动力学研究，并且提供了关于非均匀时空中标量平均性质的有价值的理论见解。 那些在FLRW模型中共有的协变标量的q-平均值（"q-标量"）恒满足FLRW演化定律，并为每个区域确定一个唯一的FLRW背景状态。 所有曲率和运动学的本征张量及其不变收缩都可以用q-标量及其线性和二次局部波动来表示，这些波动通过Weyl曲率不变量与Ricci曲率不变量的比值以及径向梯度的大小传达非均匀性的影响。 我们还定义了与整个区域或时间片分配的FLRW参考平均值的"对比"直观概念相关的非局部波动。 局部和非局部二次波动的q-平均值直接且精确地与密度和哈勃膨胀标量的统计相关矩有关。 q-标量和适当定义的扰动的演化方程完全决定了模型的动力学，而无需布赫特的平均的反作用相关项。 可以在与q-标量相关的正式FLRW背景状态下定义精确球对称非线性扰动的严格形式，从而在适当极限下恢复线性扰动理论的标准结果。 我们简要探讨了该形式在开放理论问题上的可能应用，例如非均匀性的增长与引力熵定义之间的关系。 显示英文摘要

摘要： We introduce a scalar weighed average ("q-average") acting on concentric comoving domains in spherically symmetric Lemaitre-Tolman-Bondi (LTB) dust models. The resulting averaging formalism allows for an elegant coordinate independent dynamical study of the models, providing as well a valuable theoretical insight on the properties of scalar averaging in inhomogeneous spacetimes. The q-averages of those covariant scalars common to FLRW models (the "q-scalars") identically satisfy FLRW evolution laws and determine for every domain a unique FLRW background state. All curvature and kinematic proper tensors and their invariant contractions are expressible in terms of the q-scalars and their linear and quadratic local fluctuations, which convey the effects of inhomogeneity through the ratio of Weyl to Ricci curvature invariants and the magnitude of radial gradients. We define also non-local fluctuations associated with the intuitive notion of a "contrast" with respect to FLRW reference averaged values assigned to a whole domain or time slice. The q-averages of local and non-local quadratic fluctuations are directly and exactly related to statistical correlation moments of the density and Hubble expansion scalar. The evolution equations for the q-scalars and suitably defined perturbations completely determine the dynamics of the models without the back-reaction correlation terms of Buchert's average. A rigorous formalism of exact spherical non-linear perturbations can be defined over a formal FLRW background state associated to the q-scalars, recovering the standard results of linear perturbation theory in the appropriate limit. We briefly explore the possible application of this formalism to open theoretical issues, such as the relation between the growth of inhomogeneity and a definition of gravitational entropy.