Yang–Mills monopoles in extremal Reissner–Nordström black hole metric

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