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arXiv 1801.02249gr-qc
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FRW宇宙中一个小块的质量

Mass of a Patch of an FRW Universe

Sarah R. Geller, Jolyon K. Bloomfield, Alan H. Guth

摘要:

1963年,泽尔多维奇设计了一种方法来定义封闭的弗里德曼-罗伯逊-沃克(FRW)宇宙的质量,并表明根据这个定义,它正好是零。在这个结果的基础上,我们证明了平坦和开放宇宙的质量是(毫不奇怪的)发散的。我们还提出了封闭形式的解决方案,为每一类曲率的均匀无压灰尘的有限球形补丁的边界的轨迹,探索详细的动态边界。在所有情况下,FRW补丁都是从白洞中出现的。在封闭的情况下,斑块在收缩并进入黑洞之前会膨胀到最大半径,而平坦和开放的FRW斑块则会无限膨胀。我们将我们的结果与牛顿宇宙学的经典预期进行比较,表明对于小半径,牛顿能量对静止质量能量给出了领先的修正。

英文摘要:

In 1963, Zel'dovich devised a method to define the mass of a closed Friedmann-Robertson-Walker (FRW) universe, showing that by this definition it is exactly zero. Rounding out this result, we show that the masses of flat and open universes are (unsurprisingly) divergent. We also present closed-form solutions for the trajectory of the boundary of a finite spherical patch of homogeneous pressureless dust for each class of curvature, exploring the dynamics of the boundary in detail. In all cases, the FRW patch emerges from a white hole. In the closed case, the patch expands to a maximum radius before contracting and entering a black hole, while flat and open FRW patches expand without bound. We compare our results to the classical expectations of Newtonian cosmology, showing that for small radii the Newtonian energy gives the leading correction to the rest mass energy.

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