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

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.

35 pages, 14 figures

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Cited by in corpus (10)

• Kerr black holes with synchronised scalar hair and higher azimuthal harmonic index
• No hair theorem for spherically symmetric regular compact stars with Dirichlet boundary conditions
• Spinning gravitating Skyrmions in generalized Einstein-Skyrme model
• On the effects of the Chern-Simons term in an Abelian gauged Skyrme model in $d=4+1$ dimensions
• $SO(2)$ gauged Skyrmions in $4+1$ dimensions
• Exact flavored black $p$-branes and self-gravitating instantons from toroidal black holes with Skyrme hair
• A no-go theorem for scalar fields with couplings from Ginzburg-Landau models
• No scalar condensations outside reflecting stars with coupling terms from Ginzburg-Landau models
• Analytical investigations on non-minimally coupled scalar fields outside neutral reflecting shells
• Radial Stabilization of Magnetic Skyrmions Under Strong External Magnetic Field