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

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