SU(2) Cosmological Solitons

Abstract

We present a class of numerical solutions to the SU(2) nonlinear $\sigma$-model coupled to the Einstein equations with cosmological constant $\Lambda \ge 0$ in spherical symmetry. These solutions are characterized by the presence of a regular static region which includes a center of symmetry. They are parameterized by a dimensionless ``coupling constant'' $\beta$, the sign of the cosmological constant, and an integer ``excitation number'' $n$. The phenomenology we find is compared to the corresponding solutions found for the Einstein-Yang-Mills (EYM) equations with positive $\Lambda$ (EYM$\Lambda$). If we choose $\Lambda$ positive and fix $n$, we find a family of static spacetimes with a Killing horizon for $0\le \beta <{\beta }_{max}$. As a limiting solution for $\beta ={\beta }_{max}$ we find a {\em globally} static spacetime with $\Lambda =0$, the lowest excitation being the Einstein static universe. To interpret the physical significance of the Killing horizon in the cosmological context, we apply the concept of a trapping horizon as formulated by Hayward. For small values of $\beta$ an asymptotically de Sitter dynamic region contains the static region within a Killing horizon of cosmological type. For strong coupling the static region contains an ``eternal cosmological black hole''.

20 pages, 6 figures, Revtex

References in corpus (2)

• Gravitating Non-Abelian Solitons and Black Holes with Yang-Mills Fields
• Sigma Model on de Sitter Space

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