Instability of infinitely many stationary solutions of the SU(2) Yang-Mills fields on the exterior of the Schwarzschild black hole

TL;DR

This paper investigates the stability of stationary solutions of spherically symmetric SU(2) Yang-Mills fields on Schwarzschild black holes, revealing infinitely many solutions that are all nonlinearly unstable, highlighting their potential physical significance.

Contribution

It demonstrates the existence of infinitely many stationary solutions of SU(2) Yang-Mills fields on Schwarzschild spacetime and proves their nonlinear instability.

Findings

Countable set of stationary solutions identified

All solutions are nonlinearly unstable

Implications for black hole physics and gauge field dynamics

Abstract

We consider the spherically symmetric SU(2) Yang-Mills Fields on the Schwarzschild metric. Within the so called purely magnetic Ansatz we show that there exists a countable number of stationary solutions which are all nonlinearly unstable.