Cylindrically symmetric solitons in Einstein-Yang-Mills theory

Abstract

Recently new Einstein-Yang-Mills (EYM) soliton solutions were presented which describe superconducting strings with Kasner asymptotic (hep-th/0610183). Here we study the static cylindrically symmetric SU(2) EYM system in more detail. The ansatz for the gauge field corresponds to superposition of the azimuthal $B_{\varphi }$ and the longitudinal $B_z$ components of the color magnetic field. We derive sum rules relating data on the symmetry axis to asymptotic data and show that generic asymptotic structure of regular solutions is Kasner. Solutions starting with vacuum data on the axis generically are divergent. Regular solutions correspond to some bifurcation manifold in the space of parameters which has the low-energy limiting point corresponding to string solutions in flat space (with the divergent total energy) and the high-curvature point where gravity is crucial. Some analytical results are presented for the low energy limit, and numerical bifurcation curves are constructed in the gravitating case. Depending on the parameters, the solution looks like a straight string or a pair of straight and circular strings. The existence of such non-linear superposition of two strings becomes possible due to self-interaction terms in the Yang-Mills action which suppress contribution of the circular string near the polar axis.

21 pages, 11 figures

References in corpus (14)

• Cylindrical Black Hole in General Relativity
• Gravitating Non-Abelian Solitons and Black Holes with Yang-Mills Fields
• Non-Abelian Solitons in N=4 Gauged Supergravity and Leading Order String Theory
• Static Axially Symmetric Einstein-Yang-Mills-Dilaton Solutions: I.Regular Solutions
• Gravitational waves, black holes and cosmic strings in cylindrical symmetry
• Non-abelian 4-d black holes, wrapped 5-branes, and their dual descriptions
• Complete Classification of the String-like Solutions of the Gravitating Abelian Higgs Model
• Gravitating Yang-Mills vortices in 4+1 spacetime dimensions
• Ultrarelativistic black hole in an external electromagnetic field and gravitational waves in the Melvin universe
• Axially Symmetric Multisphalerons in Yang-Mills-Dilaton Theory
• Cosmic Strings in the Abelian Higgs Model with Conformal Coupling to Gravity
• Melvin solution with a dilaton potential
• Physical Interpretation of Cylindrically Symmetric Static Gravitational Fields
• Self-Gravitating Non-Abelian Cosmic String Solution

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