Some Remarks on Gravitational Global Monopoles

TL;DR

This paper analytically derives the maximum vacuum Higgs field value for static gravitational global monopoles and explores their bifurcation with de Sitter solutions and stability properties.

Contribution

It provides the exact analytical relation for the maximal Higgs field value and analyzes the stability and bifurcation of solutions in gravitational monopoles.

Findings

Derived the exact maximum Higgs field value $oxed{rac{ ext{sqrt}(3/8 ext{pi})}}$

Identified bifurcation point with de Sitter solutions at this maximum

Analyzed stability properties of the solutions

Abstract

Using mainly analytical arguments, we derive the exact relation $\eta_{max}=\sqrt{3/8\pi}$ for the maximal vacuum value of the Higgs field for static gravitational global monopoles. For this value, the global monopole bifurcates with the de Sitter solution obtained for vanishing Higgs field. In addition, we analyze the stability properties of the solutions.