What is the asymptotic future of a scalar-field model if the assumption of isotropy is relaxed in generic, homogeneous space-times with general relativity? This paper is a continuation of our previous work on Bianchi cosmologies with a $p$-form field (where $p\,\in\,\{1,3\}$)---or equivalently: an inhomogeneous, mass-less scalar gauge field with a homogeneous gradient. In this work we investigate such matter sector in General Relativity, and restrict to space-times of the particular Bianchi types VI$_0$ and VI$_{\tilde{h}}$, where $\tilde{h}=h<0\,\cap\,\neq\,-1/9\,\cup\,-1$. We show that the previously found fabric of exact solutions named Wonderland are future attractors in $\mathcal{B}$(VI$_0$) and $\mathcal{B}$(VI$_{\tilde{h}}$), extending the Collins perfect-fluid equilibrium set to include a $p$-form (with $p\,\in\,\{1,3\}$). We also write down the line-element corresponding to Wonderland in VI$_{\tilde{h}}$ and give explicit expressions for the underling gauge-potential $\phi(t,\mathbf{x})$ corresponding to this solution. Simulation of a path approaching Wonderland in Bianchi type I is also given.

中文翻译：

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柯林斯梦游仙境

如果各向同性假设在广义、同质时空和广义相对论中放宽，标量场模型的渐近未来是什么？这篇论文是我们之前关于具有 $p$-form 场（其中 $p\,\in\,\{1,3\}$）的 Bianchi 宇宙学研究的延续——或者等效地：一个不均匀的质量——具有均匀梯度的较少标量规范场。在这项工作中，我们在广义相对论中研究了这样的物质部门，并限制了特定 Bianchi 类型 VI$_0$ 和 VI$_{\tilde{h}}$ 的时空，其中 $\tilde{h}=h< 0\,\cap\,\neq\,-1/9\,\cup\,-1$。我们表明，先前发现的名为 Wonderland 的精确解结构是 $\mathcal{B}$(VI$_0$) 和 $\mathcal{B}$(VI$_{\tilde{h}}$) 中的未来吸引子，扩展柯林斯完美流体平衡集以包括 $p$-形式（具有 $p\,\in\,\{1,3\}$）。我们还写下了 VI$_{\tilde{h}}$ 中对应 Wonderland 的线元素，并给出对应于该解的下层规范势 $\phi(t,\mathbf{x})$ 的显式表达式. 还给出了在 Bianchi 类型 I 中接近仙境的路径的模拟。