We consider smooth Gowdy-symmetric generalised Taub–NUT solutions, a class of inhomogeneous cosmological models with spatial three-sphere topology. They are characterised by existence of a smooth past Cauchy horizon and, with the exception of certain singular cases, they also develop a regular future Cauchy horizon. Several examples of exact solutions were previously constructed, where the initial data (in form of the initial Ernst potentials) are polynomials of low degree. Here, we generalise to polynomial initial data of arbitrary degree. Utilising methods from soliton theory, we obtain a simple algorithm that allows us to construct the resulting Ernst potential with purely algebraic calculations. We also derive an explicit formula in terms of determinants, and we illustrate the method with two examples.

中文翻译：

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具有多项式初始数据的平滑 Gowdy 对称广义 Taub-NUT 解


我们考虑平滑 Gowdy 对称广义 Taub-NUT 解，这是一类具有空间三球拓扑结构的非均匀宇宙学模型。它们的特点是存在平滑的过去柯西视界，除了某些奇异的情况外，它们还发展出一个规则的未来柯西视界。之前构建了几个精确解的示例，其中初始数据（以初始 Ernst 势的形式）是低次多项式。在这里，我们推广到任意次数的多项式初始数据。利用孤子理论的方法，我们得到了一个简单的算法，允许我们用纯粹的代数计算来构造得到的恩斯特势。我们还根据行列式推导出了一个显式公式，并用两个例子来说明该方法。