In this work, we revisit the shear-free conjecture of general relativity and study the well-known shear-free condition in the context of the Chaplygin-gas cosmology. It had been shown in previous investigations that, in the general relativistic framework, the matter congruences of shear-free perfect fluid spacetimes should be either expansion-free or rotation-free. Our current investigation, however, indicates that a universe dominated by a Chaplygin-gas can allow a simultaneous expansion and rotation of the fluid provided that certain non-trivial conditions, which we derive and describe in what follows, are met. We also show that, in the appropriate limiting cases, our results reduce to the expected results of dust spacetimes which can only expand or rotate, but not both, at the same time.

中文翻译：

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Chaplygin 气体主导宇宙的无剪切条件

在这项工作中，我们重新审视了广义相对论的无剪切猜想，并在查普利金气体宇宙学的背景下研究了众所周知的无剪切条件。先前的研究表明，在广义相对论框架中，无剪切完美流体时空的物质同余应该是无膨胀或无旋转的。然而，我们目前的研究表明，只要满足我们在下文中推导和描述的某些非平凡条件，一个由 Chaplygin 气体主导的宇宙可以允许流体同时膨胀和旋转。我们还表明，在适当的极限情况下，我们的结果减少到尘埃时空的预期结果，尘埃时空只能膨胀或旋转，但不能同时膨胀或旋转。