标题： SU(2) 宇宙学孤立子 显示英文标题

标题： SU(2) Cosmological Solitons

摘要： 我们提出了一类SU(2)非线性$\sigma$模型与带有宇宙学常数$\Lambda\geq 0$的爱因斯坦方程在球对称情况下的数值解。这些解的特点是存在一个包含对称中心的规则静态区域。它们由一个无量纲的“耦合常数”$\beta$、宇宙学常数的符号以及一个整数“激发数”$n$来参数化。我们发现的现象与在正$\Lambda$（EYM$\Lambda$）情况下找到的相应解进行了比较。 如果我们选择$\Lambda$为正并固定$n$，我们得到一个具有 Killing 视界对于$0 \leq \beta < \beta_{max}$的静态时空族。 作为$\beta = \beta_{max}$的极限解，我们找到一个{\em 全局地}的静态时空，具有$\Lambda=0$，最低激发态是爱因斯坦静态宇宙。 为了在宇宙学背景下解释 Killing 视界物理意义，我们应用 Hayward 提出的捕获视界的概念。 对于$\beta$的小值，渐近于 de Sitter 的动态区域包含在宇宙学类型的 Killing 视界内的静态区域。 对于强耦合，静态区域包含一个“永恒宇宙黑洞”。 显示英文摘要

摘要： We present a class of numerical solutions to the SU(2) nonlinear $\sigma$-model coupled to the Einstein equations with cosmological constant $\Lambda\geq 0$ 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 $0 \leq \beta < \beta_{max}$. 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''.