带电初始数据集的次优彭罗斯不等式
The suboptimal Penrose inequality for charged initial data sets
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中文总结 AI 辅助
本文证明带电渐近平坦初始数据集满足含电荷的次优彭罗斯不等式，并推广至双曲情形及轴对称含角动量情形。
中文摘要 AI 辅助
给定一个完整的、三维的、渐近平坦的爱因斯坦-麦克斯韦方程初始数据集，且磁场为零，我们证明存在一个小的普适常数$\mathcal{C}$，使得$m\geq\mathcal{C}(\sqrt{\mathcal{A}/(16\pi)}+\mathcal{Q}^2\sqrt{\pi/\mathcal{A}}\\,)$成立。类似陈述对渐近双曲初始数据集也成立，其中ADM质量由双曲能量替代。在额外的轴对称假设下，该不等式可进一步加强以包含角动量。这些结果将Allen-Bryden-Kazaras-Khuri最近获得的彭罗斯型不等式推广到带电情形。
英文摘要
Given a complete, 3-dimensional, asymptotically flat initial data set for the Einstein-Maxwell equations with vanishing magnetic field, we show that there exists a small universal constant $\mathcal{C}$ such that $m\geq\mathcal{C}(\sqrt{\mathcal{A}/(16π)}+\mathcal{Q}^2\sqrt{π/\mathcal{A}}\,)$. An analogous statement holds for asymptotically hyperboloidal initial data sets with the ADM mass replaced by hyperbolic energy. Under the additional assumption of axisymmetry, the inequality may be further strengthened to include angular momentum. These results extend the Penrose-type inequalities recently obtained by Allen-Bryden-Kazaras-Khuri to the charged setting.
