Perturbations of global monopoles as a black hole's hair

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 vacuumexpectation value of the scalar field. When the vacuum expectation value is larger than a certaincritical value, this spacetime has a cosmological event horizon. We investigate the stability of thesesolutions against the spherical and polar perturbations and confirm that the global monopole hair is stablein 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 andviolation of the black hole no-hair conjecture in asymptotically non-flat spacetime.