Einstein–Maxwell理论中静电电容器的模型
Model for an electrostatic capacitor in Einstein-Maxwell theory
AI总结：
研究构建了Einstein–Maxwell理论下的平行板静电电容器模型，通过切除VŽ解的奇点区并粘合到渐近平直外部时空，说明强电场可产生引力效应。
摘要：
本文提出了一种平行板静电电容器的广义相对论模型。该时空是Einstein–Maxwell方程的解，并涉及此前由Veselý和Žofka（VŽ）研究过的一类解。具体而言，包含曲率奇点的部分被切除，剩余的正则区域被粘合到渐近Minkowski时空。本质上，这产生了一个弯曲的电真空VŽ时空，其两侧夹有电磁场为零的外部时空。连接条件要求边界上存在带电物质。我们将该构型解释为一个平行板电容器，其引力效应由强电场诱导。本文还简要考虑了球形电容器。
英文摘要：
A general relativistic model of a parallel-plate electrostatic capacitor is presented. The spacetime is a solution to the Einstein--Maxwell equations and involves class of solution previously studied by Veselý and Žofka (VŽ). In particular, the parts containing curvature singularities are cut out and the remaining regular section is glued to asymptotically-Minkowski spacetimes. In essence, this results in a curved electro-vacuum VŽ spacetime sandwiched on both sides by exterior spacetimes with vanishing electromagnetic fields. Junction conditions require the presence of charged matter on the boundaries. We interpret this configuration as a parallel-plate capacitor with gravitational effects induced by the strong electric fields. The spherical capacitor is briefly considered.
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