Small and hollow magnetic monopoles

TL;DR

This paper explores generalized non-Abelian magnetic monopoles, discovering two new classes—small monopoles and hollow monopoles—with unique energy density profiles and size characteristics influenced by model parameters.

Contribution

It introduces two novel monopole solutions in a generalized non-Abelian model, expanding understanding of monopole structures beyond the standard 't Hooft-Polyakov monopole.

Findings

Identified analytical solutions for small monopoles.

Discovered hollow monopoles with a core energy density hole.

Showed monopole size depends on magnetic permeability parameter.

Abstract

We deal with the presence of magnetic monopoles in a non Abelian model that generalizes the standard 't~Hooft-Polyakov model in three spatial dimensions. We investigate the energy density of the static and spherically symmetric solutions to find first order differential equations that solve the equations of motion. The system is further studied and two distinct classes of solutions are obtained, one that can also be described by analytical solutions which is called small monopole, since it is significantly smaller than the standard 't~Hooft-Polyakov monopole. The other type of structure is the hollow monopole, since the energy density is endowed with a hole at its core. The hollow monopole can be smaller or larger than the standard monopole, depending on the value of the parameter that controls the magnetic permeability of the model.