论文标题
非权利主义政权和拓扑：爱因斯坦方程中的拓扑术语
Non-relativistic regime and topology: topological term in the Einstein equation
论文作者
论文摘要
我们研究相对论空间的非权利主义（NR）限制，与宇宙的拓扑相关。我们首先表明，爱因斯坦方程的NR极限仅在欧几里得拓扑中才有可能，即，覆盖空间为$ \ mathbb {e}^3 $。我们将此结果解释为非欧盟拓扑中一般相对论的不一致，并提出了对该理论的修改，该理论允许在任何拓扑中执行极限。为此，除了物理时空连接外，还引入了第二个参考非动力连接。参考连接的选择与时空拓扑的覆盖空间有关。修改后的爱因斯坦方程不仅具有物理时空的RICCI张量，还具有物理和参考ricci张量之间的差异。如果一个人想研究具有非欧国人拓扑的模型宇宙并承认非相关性极限，则应将该理论视为一般相对论。
We study the non-relativistic (NR) limit of relativistic spacetimes in relation with the topology of the Universe. We first show that the NR limit of the Einstein equation is only possible in Euclidean topologies, i.e. for which the covering space is $\mathbb{E}^3$. We interpret this result as an inconsistency of general relativity in non-Euclidean topologies and propose a modification of that theory which allows for the limit to be performed in any topology. For this, a second reference non-dynamical connection is introduced in addition to the physical spacetime connection. The choice of reference connection is related to the covering space of the spacetime topology. Instead of featuring only the physical spacetime Ricci tensor, the modified Einstein equation features the difference between the physical and the reference Ricci tensors. This theory should be considered instead of general relativity if one wants to study a model universe with a non-Euclidean topology and admitting a non-relativistic limit.
