Backreaction and continuum limit in a closed universe filled with black holes
Backreaction and continuum limit in a closed universe filled with black holes
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充满黑洞的封闭宇宙中的反反应和连续极限
DOI：
10.1088/0264-9381/31/8/085002
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发表时间：
2013
影响因子：
3.5
通讯作者：
Mikolaj Korzy'nski
中科院分区：
文献类型：
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作者：
Mikolaj Korzy'nski
本文讨论了以黑洞为唯一引力场源的真空封闭宇宙学模型的初始数据的连续极限。我们考虑的模型是约束方程的精确解，代表了一个真空宇宙，其中一些黑洞被放置在S3拓扑的空间切片上，当黑洞处于静止状态时，在其最大膨胀的时刻被考虑。我们解释了如何以及在什么条件下弗里德曼Lemaintre-Robertson-步行者（FLRW）度规出现的连续极限时，包含在模型中的黑洞的数量趋于无穷大。我们还讨论了模型的有效宇宙学参数之间的关系，推断从大尺度几何的时空，和个别黑洞的质量。特别是，我们证明了系统的总有效质量和所有黑洞的质量之和之间的差异的估计，从而量化的物质分布或宇宙学的逆反应的不均匀性的影响。
We discuss the continuum limit of the initial data for a vacuum, closed cosmological model with black holes as the only sources of the gravitational field. The model we consider is an exact solution of the constraint equations and represents a vacuum universe with a number of black holes placed on a spatial slice of S3 topology considered at the moment of its largest expansion when the black holes are momentary at rest. We explain how and under what conditions the Friedmann–Lemaître–Robertson–Walker (FLRW) metric arises as the continuum limit when the number of black holes contained in the model goes to infinity. We also discuss the relation between the effective cosmological parameters of the model, inferred from the large scale geometry of the spacetime, and the masses of individual black holes. In particular, we prove an estimate for the difference between the total effective mass of the system and the sum of the masses of all black holes, thus quantifying the effects of the inhomogeneities in the matter distribution or the cosmological backreaction.