Gravitating BPS Skyrmions

TL;DR

This paper extends the BPS Skyrme model to curved spacetimes, deriving exact solutions on spheres and hyperboloids, and explores gravitating Skyrmions in anti-de Sitter and de Sitter spaces, including numerical analysis.

Contribution

It generalizes the BPS Skyrme model to curved spacetime, providing exact solutions and analyzing gravitating Skyrmions with and without backreaction.

Findings

Exact solutions on 3-sphere and hyperboloid

Analytic gravitating Skyrmion on 3-sphere

Numerical solutions match analytic ones at weak coupling

Abstract

The BPS Skyrme model has many exact analytic solutions in flat space. We generalize the model to a curved space or spacetime and find that the solutions can only be BPS for a constant time-time component of the metric tensor. We find exact solutions on the curved spaces: a 3-sphere and a 3-hyperboloid; and we further find an analytic gravitating Skyrmion on the 3-sphere. For the case of a nontrivial time-time component of the metric, we suggest a potential for which we find analytic solutions on anti-de Sitter and de Sitter spacetimes in the limit of no gravitational backreaction. We take the gravitational coupling into account in numerical solutions and show that they are well approximated by the analytic solutions for weak gravitational coupling.