Skyrmions, Skyrme stars and black holes with Skyrme hair in five spacetime dimension

TL;DR

This paper extends the Skyrme model to five dimensions, discovering regular Skyrmions, Skyrme stars, and rotating black holes with Skyrme hair, and compares these solutions with scalar field models like boson stars.

Contribution

It introduces a five-dimensional Skyrme model with new regular solutions and rotating black holes with Skyrme hair, highlighting the importance of synchronization in rotating hairy black holes.

Findings

Found regular Skyrmions and Skyrme stars in 5D

Constructed black holes with Skyrme hair and rotation

Compared Skyrme solutions with scalar field models

Abstract

We consider a class of generalizations of the Skyrme model to five spacetime dimensions ($d=5$), which is defined in terms of an $O(5)$ sigma model. A special ansatz for the Skyrme field allows angular momentum to be present and equations of motion with a radial dependence only. Using it, we obtain: 1) everywhere regular solutions describing localised energy lumps (Skyrmions); 2) Self-gravitating, asymptotically flat, everywhere non-singular solitonic solutions (Skyrme stars), upon minimally coupling the model to Einstein's gravity; 3) both static and spinning black holes with Skyrme hair, the latter with rotation in two orthogonal planes, with both angular momenta of equal magnitude. In the absence of gravity we present an analytic solution that satisfies a BPS-type bound and explore numerically some of the non-BPS solutions. In the presence of gravity, we contrast the solutions to this model with solutions to a complex scalar field model, namely boson stars and black holes with synchronised hair. Remarkably, even though the two models present key differences, and in particular the Skyrme model allows static hairy black holes, when introducing rotation, the synchronisation condition becomes mandatory, providing further evidence for its generality in obtaining rotating hairy black holes.