Instability of hairy black holes in spontaneously-broken Einstein-Yang-Mills-Higgs systems

TL;DR

This paper investigates the stability of hairy black holes in Einstein-Yang-Mills-Higgs systems, demonstrating their inherent instability through a novel Schrödinger-type perturbation analysis that does not require explicit solutions.

Contribution

It introduces a generalized method to analyze linear stability of black holes in complex field systems without needing explicit solutions.

Findings

Bound states in perturbation equations indicate instability.

Method applies to a broad class of hairy black holes.

No detailed black hole solutions are necessary for stability analysis.

Abstract

The stability of a new class of hairy black hole solutions in the coupled system of Einstein-Yang-Mills-Higgs is examined, generalising a method suggested by Brodbeck and Straumann and collaborators, and Volkov and Gal'tsov. The method maps the algebraic system of linearised radial perturbations of the various field modes around the black hole solution into a coupled system of radial equations of Schr\"odinger type. No detailed knowledge of the black hole solution is required, except from the fact that the boundary conditions at the physical space-time boundaries (horizons) must be such so as to guarantee the {\it finiteness} of the various expressions involved. In this way, it is demonstrated that the above Schr\"odinger equations have bound states, which implies the instability of the associated black hole solution.