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arXiv · 2012.12452

Yang--Mills Monopoles in Extremal Reissner--Nordstr\"{o}m Black Hole Metric

Xiangqin Zhang·Yisong Yang
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Abstract

We show that the closed-form monotone solution linking two different vacuum states, for the exterior Yang--Mills wave equation over the extremal Reissner--Nordstr\"{o}m spacetime found in a recent work of Bizo\'{n} and Kahl, 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 consideration.

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Xiangqin Zhang, Yisong Yang. 2020-12-23. Yang--Mills Monopoles in Extremal Reissner--Nordstr\"{o}m Black Hole Metric. https://doi.org/10.1063/5.0046290

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