Analytical solutions for Maxwell-scalar system on radially symmetric spacetimes

TL;DR

This paper derives analytical solutions for Maxwell-scalar systems on radially symmetric spacetimes, exploring conditions for minimal energy configurations, stability, and mapping to kink solutions in lower dimensions.

Contribution

It introduces a formalism to find analytical solutions for Maxwell-scalar models on symmetric spacetimes and establishes their stability and energy properties.

Findings

Analytical solutions for specific spacetimes are obtained.

Energy density of solutions is finite.

Solutions obeying the first-order equations are stable.

Abstract

We investigate Maxwell-scalar models on radially symmetric spacetimes in which the gauge and scalar fields are coupled via the electric permittivity. We find the conditions that allow for the presence of minimum energy configurations. In this formalism, the charge density must be written exclusively in terms of the components of the metric tensor and the scalar field is governed by first-order equations. We also find a manner to map the aforementioned equation into the corresponding one associated to kinks in $(1,1)$ spacetime dimensions, so we get analytical solutions for three specific spacetimes. We then calculate the energy density and show that the energy is finite. The stability of the solutions against contractions and dilations, following Derrick's argument, and around small fluctuations in the fields is also investigated. In this direction, we show that the solutions obeying the first-order framework are stable.