Global Monopole in General Relativity

TL;DR

This paper studies the gravitational effects of global monopoles within general relativity, classifying solution behaviors, confirming known properties, and discovering new solutions with oscillating Higgs fields and specific energy bounds.

Contribution

It provides a comprehensive classification of monopole solutions, analytically confirms properties for the Mexican hat potential, and introduces new oscillating Higgs field solutions with horizons and singularities.

Findings

Solutions with finite energy exist only for 1<γ<3

Monotonically growing Higgs field solutions are confirmed

New oscillating Higgs field solutions with multiple knots are found

Abstract

We consider the gravitational properties of a global monopole on the basis of the simplest Higgs scalar triplet model in general relativity. We begin with establishing some common features of hedgehog-type solutions with a regular center, independent of the choice of the symmetry-breaking potential. There are six types of qualitative behavior of the solutions; we show, in particular, that the metric can contain at most one simple horizon. For the standard Mexican hat potential, the previously known properties of the solutions are confirmed and some new results are obtained. Thus, we show analytically that solutions with monotonically growing Higgs field and finite energy in the static region exist only in the interval $1<\gamma <3$, $\gamma $ being the squared energy of spontaneous symmetry breaking in Planck units. The cosmological properties of these globally regular solutions apparently favor the idea that the standard Big Bang might be replaced with a nonsingular static core and a horizon appearing as a result of some symmetry-breaking phase transition on the Planck energy scale. In addition to the monotonic solutions, we present and analyze a sequence of families of new solutions with oscillating Higgs field. These families are parametrized by $n$, the number of knots of the Higgs field, and exist for $\gamma < \gamma_n = 6/[(2n+1) (n+2)]$; all such solutions possess a horizon and a singularity beyond it.