标题： 广义相对论的非线性效应来自多尺度结构 显示英文标题

标题： Nonlinear effects of general relativity from multiscale structure

摘要： 广义相对论的非线性效应在天体物理环境中何时起作用？ 显然，对于引力场的非常致密的源（例如中子星或黑洞）来说，它们显然是相关的。 在这篇论文中，我讨论了另一种不太明显的情况，在这种情况下，由于物质分布具有复杂的多尺度结构，可能会产生大的相对论效应。 我给出了一个精确解，其能量密度分布呈现为一系列嵌套的空洞和不同大小的过密区域的层次结构，从均匀性尺度延伸到任意小的尺度。 我证明了尽管每个空洞和过密区域看起来都非常弱的相对论效应，因此可以使用线性化的广义相对论来描述，但整体解实际上处于非线性区域。 当我们将解的ADM质量和局部质量密度的积分进行比较时，最能清楚地看到其非线性性质：它们之间的差异，即相对论质量亏损，在不均匀性扩展到足够小尺度的情况下可能显著。 质量的非可加性意味着存在大的反作用效应，即平均的大尺度有效应力-能量张量与局部能量密度的简单平均之间存在显著差异。 我还展示了这是由于不均匀且多尺度的结构而产生的广义相对论效应。 我还讨论了这些结果在宇宙学和相对论天体物理学中的相关性。 显示英文摘要

摘要： When do the nonlinear effects of general relativity matter in astrophysical situations? They are obviously relevant for very compact sources of the gravitational field, such as neutron stars or black holes. In this paper I discuss another, less obvious situation, in which large relativistic effects may arise due to a complicated, multiscale structure of the matter distribution. I present an exact solution with an inhomogeneous energy density distribution in the form of a hierarchy of nested voids and overdensities of various sizes, extending from the homogeneity scale down to arbitrary small scales. I show that although each of the voids and overdensities seems to be very weakly relativistic, and thus easy to describe using the linearized general relativity, the solution taken as a whole lies in fact in the nonlinear regime. Its nonlinear properties are most easily seen when we compare the ADM mass of the solution and the integral of the local mass density: the difference between them, i.e. the relativistic mass deficit, can be significant provided that the inhomogeneities extend to sufficiently small scales. The non-additivity of masses implies a large backreaction effect, i.e. significant discrepancy between the averaged, large-scale effective stress-energy tensor and the naive average of the local energy density. I show that this is a general relativistic effect arising due to the inhomogeneous, multiscale structure. I also discuss the relevance of the results in cosmology and relativistic astrophysics.