The ideal magnetohydrodynamic theorem on the conservation of the magnetic connections between plasma elements is extended to non-ideal relativistic plasmas in curved spacetime. The existence of generalized magnetofluid connections that are preserved by the plasma dynamics is formalized by means of a covariant connection equation that includes different non-ideal effects. These generalized connections are constituted by 2-dimensional hypersurfaces, which are linked to an antisymmetric tensor field that unifies the electromagnetic and fluid fields. They can be interpreted in terms of generalized magnetofluid vorticity field lines by considering a $3+1$ foliation of spacetime and a time resetting projection that compensates for the loss of simultaneity between spatially separated events. The worldsheets of the generalized magnetofluid vorticity field lines play a fundamental role in the plasma dynamics by prohibiting evolutions that do not preserve the magnetofluid connectivity.

中文翻译：

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弯曲时空中的广义磁流体连接

关于等离子元素之间的磁连接守恒的理想磁流体力学定理在弯曲的时空中扩展到了非理想的相对论性等离子体。借助于包括不同的非理想效应的协变连接方程式，形式化了由等离子体动力学保留的广义磁流体连接。这些广义连接由二维超曲面构成，二维超曲面链接到统一电磁场和流场的反对称张量场。可以考虑广义磁流体旋涡场线来解释它们。$3+\mathrm{1个}$时空偏移和时间重置投影，可补偿空间分离事件之间同时发生的损失。广义磁流体涡度场线的世界表通过禁止不保留磁流体连通性的演化，在等离子体动力学中起着基本作用。