The Bartnik mass is a notion of quasi-local mass which is remarkably difficult to compute. Mantoulidis and Schoen [2016] developed a novel technique to construct asymptotically flat extensions of minimal Bartnik data in such a way that the ADM mass of these extensions is well-controlled, and thus, they were able to compute the Bartnik mass for minimal spheres satisfying a stability condition. In this work, we develop extensions and gluing tools, a la Mantoulidis and Schoen, for time-symmetric initial data sets for the Einstein-Maxwell equations that allow us to compute the value of an ad-hoc notion of charged Barnik mass for suitable charged minimal Bartnik data.

中文翻译：

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带电荷的渐近平坦扩展

Bartnik 质量是一种非常难以计算的准局部质量概念。Mantoulidis 和 Schoen [2016] 开发了一种新技术来构建最小 Bartnik 数据的渐近平坦扩展，使得这些扩展的 ADM 质量得到良好控制，因此，他们能够计算满足以下条件的最小球体的 Bartnik 质量一个稳定条件。在这项工作中，我们开发了扩展和粘合工具，la Mantoulidis 和 Schoen，用于爱因斯坦-麦克斯韦方程组的时间对称初始数据集，使我们能够计算带电巴尼克质量的临时概念的值，用于合适的带电最小的 Bartnik 数据。