BPS equations and solutions for Maxwell–scalar theory

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.