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arXiv 2005.01968astro-ph.CO
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一个无限长的物体能适应膨胀的宇宙吗？

Can an Infinitely Long Object Fit in an Expanding Universe?

Aaron Glanville, Tamara Davis

备注：
10 Pages, 6 Figures. Minor changes, additional discussion in Sections 2 and 4
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摘要：

当宇宙膨胀时，空间是否会拉伸其内容物？通常我们会说答案是否定的--空间的拉伸并不像橡胶片的拉伸那样可以拖动物体。在本文中，我们探索了一个潜在的反例--即我们证明了在膨胀的宇宙中不可能制造出任意长的物体，因为不可能让物体的远端相对于我们保持“静止”（如Friedmann-Lemaitre-Robertson-Walker度规中所定义的）。我们表明，这并不意味着，扩大的空间有一个与之相关的力，相反，一些虚拟力出现，由于我们选择的参考系。通过选择我们通常的时间片（所有随动观察者都同意宇宙的年龄），我们选择了一个与任何惯性观察者的坐标系不对应的全局坐标系。因此，简单的相对论速度变换产生了一个明显的加速度，即使在没有力存在的情况下。这种效应类似于在旋转参考系中描述物体时产生的虚拟力，如科里奥利效应的情况。

英文摘要：

Does space stretch its contents as the universe expands? Usually we say the answer is no - the stretching of space is not like the stretching of a rubber sheet that might drag things with it. In this paper we explore a potential counter example - namely we show that is is impossible to make an arbitrarily long object in an expanding universe, because it is impossible to hold the distant end of the object "stationary" with respect to us (as defined in the Friedmann-Lemaitre-Robertson-Walker metric). We show that this does not mean that expanding space has a force associated with it, rather, some fictitious forces arise due to our choice of reference frame. By choosing our usual time-slice (where all comoving observers agree on the age of the universe), we choose a global frame that does not correspond to the frame of any inertial observer. As a result, simple relativistic velocity transforms generate an apparent acceleration, even where no force exists. This effect is similar to the fictitious forces that arise in describing objects in rotating reference frames, as in the case of the Coriolis effect.

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