Kink dynamics for the Yang-Mills field in an extremal Reissner-Nordstr”om black hole

In this work we consider the Yang-Mills field in an extremal Reissner-Nordstr"om black hole. The kink is a fundamental, strongly unstable stationary solution in this non-perturbative, variable coefficients model, with a polynomial tail and no explicit form.

In this paper, we introduce and extend several virial techniques, adapt them to the inhomogeneous medium setting, and construct a finite codimensional manifold of the energy space where the kink is asymptotically stable. In particular, we handle, using virial techniques, the emergence of a weak threshold resonance in the description of the stable manifold.

Recommended citation: I. Acevedo, and C. Muñoz (2026). Kink dynamics for the Yang-Mills field in an extremal Reissner-Nordström black hole. arXiv:2501.12790v4.
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