Gravitating gauged BPS baby Skyrmions

TL;DR

This paper demonstrates that the minimally gauged BPS baby Skyrme model remains a BPS theory when coupled with gravity, with solutions characterized by topological charge and gravitational effects on mass and radius.

Contribution

It provides an exact analytical framework for understanding gravitating gauged BPS baby Skyrmions, including their mass, flux, and geometric properties as functions of topological charge.

Findings

Proper mass, magnetic flux, and volume are linear in topological charge.

Total ADM mass and radius include quadratic gravitational contributions.

Complete classification of mass-radius relations is achieved.

Abstract

We show that the minimally gauged BPS baby Skyrme model remains a BPS theory after coupling with gravity that is the topologically nontrivial configurations called baby Skyrmions carrying magnetic flux are solutions to a zero pressure equation. Following that the proper mass, magnetic flux and the proper geometric volume are linear function of the topological charge, while the total ADM mass and geometric radius get a contribution due to the gravitational interaction which 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 possible mass-radius curves is provided.As an example we consider the model with the pion like mass potential, for which, an approximated but analytical form of the superpotential is provided.