Gravitating BPS Skyrmions

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.

LaTeX: 27 pages, 6 figures; V2: typos corrected

References in corpus (6)

• Generalized Global Defect Solutions
• Skyrmions, instantons and holography
• Matryoshka Skyrmions
• BPS Skyrmions as neutron stars
• Monopoles and Holography
• Effective field theories on solitons of generic shapes

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• The BPS sectors of the Skyrme model and their non-BPS extensions
• Gravitating gauged BPS baby Skyrmions
• Analytic non-Abelian gravitating solitons in the Einstein-Yang-Mills-Higgs theory and transitions between them
• BPS deformations of the Skyrme model