Cosmological Einstein-Skyrme solutions with non-vanishing topological charge

Abstract

Time-dependent analytic solutions of the Einstein-Skyrme system --gravitating Skyrmions--, with topological charge one are analyzed in detail. In particular, the question of whether these Skyrmions reach a spherically symmetric configuration for $t\to +\infty$ is discussed. It is shown that there is a static, spherically symmetric solution described by the Ermakov-Pinney system, which is fully integrable by algebraic methods. For $\Lambda >0$ this spherically symmetric solution is found to be in a "neutral equilibrium" under small deformations, in the sense that under a small squashing it would neither blow up nor dissapear after a long time, but it would remain finite forever (plastic deformation). Thus, in a sense, the coupling with Einstein gravity spontaneously breaks the spherical symmetry of the solution. However, in spite of the lack of isotropy, for $t\to \infty$ (and $\Lambda >0$) the space time is locally flat and the anisotropy of the Skyrmion only reflects the squashing of spacetime.

arXiv comment12 pages, 6 figures, to appear in Phys. Rev. D

References in corpus (27)

• A Skyrme-type proposal for baryonic matter
• On the Stability of the Einstein Static Universe
• Analytic self-gravitating Skyrmions, cosmological bounces and AdS wormholes
• Hedgehog ansatz and its generalization for self-gravitating Skyrmions
• Non-linear superposition law and Skyrme crystals
• Exact multi-soliton solutions in the four dimensional Skyrme model
• Critical Collapse of Skyrmions
• On asymptotic stability of the Skyrmion
• Generalized Hedgehog ansatz and Gribov copies in regions with non trivial topologies
• The Instabilities of Bianchi Type IX Einstein Static Universes
• Exact Kink Solitons in Skyrme Crystals
• Towards Skyrmion Stars: Large Baryon Configurations in the Einstein-Skyrme Model
• Kantowski-Sachs Universes sourced by a Skyrme fluid
• SU(N) Multi-Skyrmions at Finite Volume
• Fermionic quantization of Hopf solitons
• Baryon chemical potential and in-medium properties of BPS skyrmions
• Cosmological dynamics of gravitating hadron matter
• Generalizing the autonomous Kepler Ermakov system in a Riemannian space
• Multi-Skyrmions with orientational moduli
• Fermionic quantization and configuration spaces for the Skyrme and Faddeev-Hopf models
• On the possibility of spinorial quantization in the Skyrme model
• Late-time tails of self-gravitating skyrmions
• Domain Wall Equations, Hessian of Superpotential, and Bogomol'nyi Bounds
• Non-existence of Skyrmion-Skyrmion and Skyrmion-anti-Skyrmion static equilibria
• Exact solution of the Einstein-Skyrme model in a Kantowski-Sachs spacetime
• Structure of solutions of the Skyrme model on three-sphere. Numerical results
• Dynamics of gravitating hadron matter in Bianchi-IX cosmological model

Cited by in corpus (16)

• Topologically non-trivial configurations in the 4d Einstein--nonlinear $\sigma$-model system
• Nonlinear extensions of gravitating dyons: from NUT wormholes to Taub-Bolt instantons
• Analytic self-gravitating $4$-Baryons, traversable NUT-AdS wormholes, flat space-time multi-Skyrmions at finite volume and a novel transition in the $SU(3)$-Skyrme model
• Analytic crystals of solitons in the four dimensional gauged non-linear sigma model
• Pion crystals hosting topologically stable baryons
• New integrable models and analytical solutions in $f(R)$~cosmology with an ideal gas
• Gravitational catalysis of merons in Einstein-Yang-Mills theory
• Hairy AdS black holes with a toroidal horizon in 4D Einstein-nonlinear $\sigma$-model system
• Gravitating superconducting solitons in the (3+1)-dimensional Einstein gauged non-linear sigma-model
• Crystals of gauged solitons, force free plasma and resurgence
• Extensions of the generalized hedgehog ansatz for the Einstein-nonlinear $\sigma$-model system: black holes with NUT, black strings and time-dependent solutions
• Bianchi IX cosmologies in the Einstein-Skyrme system in a sector with non-trivial topological charge
• Projective collineations of decomposable spacetimes generated by the Lie point symmetries of geodesic equations
• Gravitating Meron-like topological solitons in massive Yang-Mills theory and the Einstein-Skyrme model
• BPS deformations of the Skyrme model
• Meronic Einstein-Yang-Mills black hole in 5D and gravitational spin from isospin effect