Gravitating gauged BPS baby Skyrmions

Abstract

We show that the minimally gauged Bogomol'nyi-Prasad-Sommerfield baby Skyrme model remains a Bogomol'nyi-Prasad-Sommerfield theory after coupling with the gravity. That is, the topologically nontrivial configurations called the baby Skyrmions and carrying a magnetic flux are solutions to a zero pressure equation. It follows that the proper mass, the magnetic flux, and the proper geometric volume are the linear functions of the topological charge, while the total Arnowitt-Deser-Misner mass and geometric radius receive a contribution due to the gravitational interaction that is quadratic in the topological charge. All these quantities are found exactly as target space integrals (averages) of the so-called superpotential. A complete classification of the possible mass-radius curves is provided. As an example, we consider the model with the pionlike mass potential, for which an approximated but analytical form of the superpotential is provided.