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arXiv · 2501.12790

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

Ignacio Acevedo·Claudio Muñoz
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Abstract

Considered in this work is the Yang-Mills field in an extremal Reissner-Nordstr\"om black hole, a physically motivated mathematical model introduced by Bizo\'n and Kahl. 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.

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Ignacio Acevedo, Claudio Muñoz. 2025-01-22. Kink dynamics for the Yang-Mills field in an extremal Reissner-Nordstr\"om black hole. https://arxiv.org/abs/2501.12790

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