AI 中文总结
该研究针对广义相对论的Bianchi-I时空，在零能量条件下证明了全方向膨胀时测地过去不完备，全方向收缩时不受此限，且不假设时空整体拓扑。
AI 中文摘要
我们证明，在零能量条件假设下，广义相对论中的Bianchi-I时空若存在宇宙在所有方向膨胀的时刻，则必然是测地过去不完备的。而始终在至少一个方向收缩的时空不受该结论限制，我们提供了一个明确的例子。本定理的一个显著特征是，它不对时空的整体拓扑做任何假设。
英文摘要
We demonstrate that a Bianchi-I spacetime in general relativity must be geodesically past-incomplete under the assumption of the null energy condition and provided there exists a time in which the universe is expanding in all directions. Spacetimes which are always contracting along at least one direction are not subject to the conclusion, and we provide an explicit example. A distinguishing feature of our theorem is that it makes no assumption on the global topology of the spacetime.
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