We prove positive mass theorem with angular momentum and charges for axially symmetric, simply connected, maximal, complete initial data sets with two ends, one designated asymptotically flat and the other either (Kaluza–Klein) asymptotically flat or asymptotically cylindrical, for $4$-dimensional Einstein–Maxwell theory and $5$-dimensional minimal supergravity theory which metrics fail to be $C^1$ and second fundamental forms and electromagnetic fields fail to be $C^0$ across an axially symmetric hypersurface $\Sigma$. Furthermore, we remove the completeness and simple connectivity assumptions in this result and prove it for manifold with boundary such that the mean curvature of the boundary is non-positive.

中文翻译：

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沿超曲面具有角的初始数据集的正质量定理

我们用轴对称、简单连接、最大、完整的初始数据集证明具有角动量和电荷的正质量定理，其两端指定渐近平坦，另一端指定为 (Kaluza–Klein) 渐近平坦或渐近圆柱，价格为 $4$-维爱因斯坦-麦克斯韦理论和 $5$ 维极小超引力理论，其度量在轴对称超曲面 $\Sigma$ 上不能为 $C^1$，第二基本形式和电磁场不能为 $C^0$。此外，我们删除了该结果中的完整性和简单连通性假设，并针对具有边界的流形证明了这一点，使得边界的平均曲率是非正的。