Gravitating Magnetic Monopole in the Global Monopole Spacetime

TL;DR

This paper investigates the gravitational and electromagnetic properties of a magnetic monopole within a global monopole spacetime, revealing a Reissner-Nordström-like structure at large distances through numerical analysis.

Contribution

It introduces a numerical study of self-gravitating magnetic monopoles in a global monopole background, highlighting their spacetime structure and the influence of parameters like vacuum expectation value and self-coupling.

Findings

Large distance spacetime resembles Reissner-Nordström with a solid angle deficit

Numerical solutions describe metric and matter fields near the monopole core

Behavior depends on Higgs vacuum expectation value and self-coupling constant

Abstract

In this paper we study the regular self-gravitating 't Hooft-Polyakov magnetic monopole in a global monopole spacetime. We show that for the large distance, the structure of the manifold corresponds to the Reissner-Nordstr\"{o}m spacetime with a solid angle deficit factor. Although we analyze static and spherically symmetric solutions, it is not possible to solve analytically the system of coupled differential equations and only numerical evaluations can provide detailed information about the behavior of this system at the neighborhood of the defect's core. So, for this reason we solve numerically the set of differential equations for the metric tensor and for the matter fields for different values of the Higgs field vacuum expectation value, $\eta$, and the self-coupling constant, $\lambda$.