BPS equations and solutions for Maxwell-scalar theory

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. (C) 2022 Elsevier Inc. All rights reserved.