Polar Perturbations of Self-gravitating Supermassive Global Monopoles

TL;DR

This paper investigates the stability of self-gravitating global monopoles and de Sitter solutions under polar perturbations, finding that monopoles remain stable while de Sitter solutions are unstable.

Contribution

It provides a comprehensive analysis of polar perturbations of supermassive global monopoles and de Sitter solutions, extending previous stability studies to include non-spherical perturbations.

Findings

Global monopoles are stable against polar perturbations.

De Sitter solutions are unstable against polar perturbations.

Stability depends on the vacuum expectation value v of the scalar field.

Abstract

Spontaneous global symmetry breaking of O(3) scalar field gives rise to point-like topological defects, global monopoles. By taking into account self-gravity,the qualitative feature of the global monopole solutions depends on the vacuum expectation value v of the scalar field. When v < sqrt{1 / 8 pi}, there are global monopole solutions which have a deficit solid angle defined at infinity. When sqrt{1 / 8 pi} <= v < sqrt{3 / 8 pi}, there are global monopole solutions with the cosmological horizon, which we call the supermassive global monopole. When v >= sqrt{3 / 8 pi}, there is no nontrivial solution. It was shown that all of these solutions are stable against the spherical perturbations. In addition to the global monopole solutions, the de Sitter solutions exist for any value of v. They are stable against the spherical perturbations when v <= sqrt{3 / 8 pi}, while unstable for v > sqrt{3 / 8 pi}. We study polar perturbations of these solutions and find that all self-gravitating global monopoles are stable even against polar perturbations, independently of the existence of the cosmological horizon, while the de Sitter solutions are always unstable.