LTB尘埃模式中的加权标量平均，第II部分：精确扰动的形式
Weighed scalar averaging in LTB dust models, part II: a formalism of exact perturbations
摘要：
我们研究了在前一篇文章（第一部分）中应用于Lemaitre-Tolman-Bondi（LTB）模型的q平均形式主义所产生的精确扰动。通过引入一个初始值参数化，我们表明，所有的LTB标量，采取FLRW“看起来像”的形式（经常使用的文献中处理LTB模型）遵循的协变标量的q-平均值是常见的FLRW模型。这些q-标量确定每个平均域一个独特的FLRW背景状态，通过Darmois匹配条件在域边界，虽然这个背景的定义并不需要一个实际的匹配FLRW区域（瑞士奶酪型模型）。局部扰动描述了从FLRW背景状态的偏差，通过协变标量的局部梯度在每个共动域的边界，而非局部扰动这样做的一个直观的概念的“对比度”的局部标量相对于FLRW参考值出现从q平均分配给整个域或整个时间片的渐近极限。我们推导出流体流动的演化方程，完全确定的动力学模型的q标量和两种类型的扰动。一个严格的形式主义的精确球形非线性扰动的定义在FLRW背景状态相关联的q标量，恢复线性微扰理论的标准结果在适当的限制。我们检查的振幅的概念，并说明本地与非本地扰动之间的差异定性图，并通过一个例子的宇宙密度空洞，从演化方程的数值解。
英文摘要：
We examine the exact perturbations that arise from the q-average formalism that was applied in the preceding article (part I) to Lemaitre-Tolman-Bondi (LTB) models. By introducing an initial value parametrization, we show that all LTB scalars that take a FLRW "look alike" form (frequently used in the literature dealing with LTB models) follow as q-averages of covariant scalars that are common to FLRW models. These q--scalars determine for every averaging domain a unique FLRW background state through Darmois matching conditions at the domain boundary, though the definition of this background does not require an actual matching with a FLRW region (Swiss cheese type models). Local perturbations describe the deviation from the FLRW background state through the local gradients of covariant scalars at the boundary of every comoving domain, while non-local perturbations do so in terms of the intuitive notion of a "contrast" of local scalars with respect to FLRW reference values that emerge from q-averages assigned to the whole domain or the whole time slice in the asymptotic limit. We derive fluid flow evolution equations that completely determine the dynamics of the models in terms of the q-scalars and both types of perturbations. A rigorous formalism of exact spherical non-linear perturbations is defined over the FLRW background state associated to the q-scalars, recovering the standard results of linear perturbation theory in the appropriate limit. We examine the notion of the amplitude and illustrate the differences between local vs non-local perturbations by qualitative diagrams and through an example of a cosmic density void that follows from the numeric solution of the evolution equations.
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