We show that the closed-form monotone solution linking two different vacuum states, for the exterior Yang–Mills wave equation over the extremal Reissner–Nordström spacetime found in the recent work of Bizoń and Kahl [Classical Quantum Gravity 33, 175013 (2016)], is the unique solution to an associated domain-wall type energy minimization problem. We also derive the accompanying interior Yang–Mills wave equation within the same formalism. We obtain a few more closed-form solutions, regular and singular, among other solutions of oscillatory behavior, and discuss several interesting features of the solutions based on some energy considerations.

中文翻译：

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极值 Reissner-Nordström 黑洞度量中的 Yang-Mills 单极子

我们展示了连接两个不同真空状态的封闭形式单调解，对于在 Bizoń 和 Kahl 最近的工作中发现的极值 Reissner-Nordström 时空中的外部 Yang-Mills 波动方程 [Classical Quantum Gravity 33 , 175013 (2016)] , 是相关畴壁型能量最小化问题的唯一解。我们还在相同的形式中推导出伴随的内部杨-米尔斯波动方程。除了振荡行为的其他解决方案之外，我们还获得了其他一些封闭形式的正则和奇异解，并基于一些能量考虑因素，讨论了该解决方案的一些有趣特征。