A class of solitons in Maxwell-scalar and Einstein-Maxwell-scalar models

TL;DR

This paper introduces a new class of regular, localized soliton solutions in Maxwell-scalar and Einstein-Maxwell-scalar models by employing specific non-minimal couplings that regularize singularities, including in flat spacetime.

Contribution

It demonstrates how to circumvent no-go theorems for EMS solitons using diverging coupling functions, leading to explicit regular solutions in flat and curved spacetimes.

Findings

Regular solitons in flat Maxwell-scalar models with explicit solutions.

Existence of self-gravitating EMS solitons with localized energy lumps.

Mechanism to de-singularize Coulomb field via non-minimal coupling.

Abstract

Recently, no-go theorems for the existence of solitonic solutions in Einstein-Maxwell-scalar (EMS) models have been established in arXiv:1902.07721. Here we discuss how these theorems can be circumvented by a specific class of non-minimal coupling functions between a real, canonical scalar field and the electromagnetic field. When the non-minimal coupling function diverges in a specific way near the location of a point charge, it regularises all physical quantities yielding an everywhere regular, localised lump of energy. Such solutions are possible even in flat spacetime Maxwell-scalar models, wherein the model is fully integrable in the spherical sector, and exact solutions can be obtained, yielding an explicit mechanism to de-singularise the Coulomb field. Considering their gravitational backreaction, the corresponding (numerical) EMS solitons provide a simple example of self-gravitating, localised energy lumps.