BPS equations and solutions for Maxwell-scalar theory

TL;DR

This paper derives BPS equations and solutions for Maxwell-scalar models, revealing a scalar soliton around electric charges, including new solutions in curved spacetime backgrounds.

Contribution

It introduces new BPS solutions in Maxwell-scalar theory, especially for overcharged objects in curved spacetime, using an auxiliary function approach.

Findings

Scalar soliton formation around electric charges.

Recovery of known solutions in flat spacetime.

New BPS solutions in Reissner-Nordstrom background.

Abstract

Energy minimizing BPS equations and solutions are obtained for a class of models in Maxwell-scalar theory, where an abelian electric charge is immersed in an effective dielectric of a real scalar field. The first order BPS equations are developed using the straightforward on-shell method introduced by Atmaja and Ramadhan. Employment of an auxiliary function of the scalar field allows a scalar potential that displays a tachyonic instability. Consequently, a nontopological scalar soliton is found to form around the charge. Examples and solutions are provided for (1) a point charge or sphere in a flat Minkowski background, and (2) an overcharged compact object in a Reissner-Nordstrom background. The solutions presented here for the former (Minkowski) case recover those that have been previously obtained, while the latter solutions are new BPS solutions.