Novel way to construct spatially localized finite energy structures

TL;DR

This paper presents a new method to construct finite energy localized structures using scalar fields, including modifications to electric properties, with stability analysis and potential for unusual electric behaviors.

Contribution

It introduces a novel potential modification for scalar fields to achieve localized finite energy solutions and explores their impact on electric properties and stability.

Findings

Successfully constructed localized finite energy structures.

Demonstrated stability under small fluctuations.

Showed electric field can point towards positive charges.

Abstract

In this work we introduce a procedure to find localized structures with finite energy. We start dealing with global monopoles, and add a new contribution to the potential of the scalar fields, to balance the contribution of the angular gradients of the fields which lead to a slow falloff in the energy density. Within the first order formalism, first order equations that are compatible with the equations of motion are obtained and the stability under small fluctuations is investigated. We then include another set of scalar fields and study how it contributes to change the profile of the localized structure. We also study how these configurations modify the electric properties of a system with a single point charge, with generalized electric permittivity controlled by scalar fields. In this new model, in particular, we show that, depending on the specific modification of the electric properties of the medium, the electric field may engender the unusual behavior of pointing towards a positive charge.