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

TL;DR

This paper studies the Yang-Mills field around an extremal Reissner-Nordström black hole, demonstrating the construction of a stable manifold for the kink solution using virial techniques in a complex, inhomogeneous setting.

Contribution

It introduces and extends virial methods to establish asymptotic stability of the kink in an inhomogeneous black hole background, a novel approach in this context.

Findings

Constructed a finite codimensional manifold where the kink is stable.

Adapted virial techniques to inhomogeneous media.

Handled threshold resonance phenomena in stability analysis.

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.