Perturbations of global monopoles as a black hole's hair

TL;DR

This paper analyzes the stability of black holes with global monopole hair, finding that such hair remains stable under perturbations and challenging the traditional no-hair conjecture in non-flat spacetimes.

Contribution

It demonstrates the stability of global monopole hair on black holes and suggests the conservation of topological charge despite the presence of event horizons.

Findings

Global monopole hair is stable against spherical and polar perturbations.

The topological charge appears conserved in black hole spacetimes with monopole hair.

The results challenge the black hole no-hair conjecture in asymptotically non-flat spacetimes.

Abstract

We study the stability of a spherically symmetric black hole with a global monopole hair. Asymptotically the spacetime is flat but has a deficit solid angle which depends on the vacuum expectation value of the scalar field. When the vacuum expectation value is larger than a certain critical value, this spacetime has a cosmological event horizon. We investigate the stability of these solutions against the spherical and polar perturbations and confirm that the global monopole hair is stable in both cases. Although we consider some particular modes in the polar case, our analysis suggests the conservation of the "topological charge" in the presence of the event horizons and violation of black hole no-hair conjecture in asymptotically non-flat spacetime.