We analyze the necessary conditions for a body to remain rigid in an expanding cosmological Universe. First, we establish the main theorems and definitions for having a rigid body in a general spacetime as well as the new concept of quasilocal rigidity. We apply the obtained results to a homogeneous universe exploring the differences with flat spacetime. We discuss how the concept of rigid body helps to understand the expansion of space in cosmology. Finally, using a rigid system as a reference frame, we calculate the gravitational energy, and we compare it with previous results in the literature.

中文翻译：

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相对论刚性系统和宇宙膨胀

我们分析了一个物体在不断膨胀的宇宙宇宙中保持刚性的必要条件。首先，我们建立了在一般时空中具有刚体的主要定理和定义以及准局部刚性的新概念。我们将获得的结果应用到同质宇宙中，探索平坦时空的差异。我们讨论刚体的概念如何帮助理解宇宙学中的空间膨胀。最后，使用刚性系统作为参考系，我们计算重力能量，并将其与文献中的先前结果进行比较。