发表机构
Institute of Mathematics of the Czech Academy of Sciences; Universidad de La Serena; Universidad de Tarapacá; Charles University; Universidade de Aveiro; University of Tartu（捷克科学院数学研究所; 拉塞雷纳大学; 塔拉帕卡大学; 查理大学; 阿威罗大学; 塔尔图大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究利用维数约化理论的隐藏对称性构建高维旋转时空，获得含双旋转参数的五维真空背景，发现其具多方向渐近结构与定向曲率奇点，还完成了该构造向高维的最大轴向延拓。
AI 中文摘要
我们利用维数约化理论的隐藏对称性，在真空广义相对论中构建高维旋转时空。直接利用陪集空间形式，在五维下沿两个独立的轴向 Killing 向量进行约化，得到 $SL(3,\mathbb{R})/SO(3)$ 西格玛模型及具有两个独立旋转参数的真实五维背景。相同变换可产生双旋转的 Schwarzschild–Tangherlini 和 Myers–Perry 几何。新背景的显著特征是其多方向渐近结构，关联的径向-角向极限揭示了在固定角的常规大半径极限下不可见的定向曲率奇点。我们进一步证明，类时测地线可在有限仿射参数内到达此类奇异渐近端点。最后，我们描述该构造向高维的最大轴向延拓：五维是完全轴向约化至三维的最大维度，而六维容许额外非平凡平移形变，更高维度仅贡献平直的旁观方向。
英文摘要
We construct higher-dimensional swirling spacetimes in vacuum General Relativity using the hidden symmetries of the dimensionally reduced theory. Working directly with the coset-space formulation, we perform in five dimensions a reduction along the two independent axial Killing vectors, obtaining an $SL(3,\mathbb{R})/SO(3)$ sigma model and a genuinely five-dimensional background with two independent swirling parameters. The same transformation yields doubly swirling Schwarzschild--Tangherlini and Myers--Perry geometries. A distinctive feature of the new background is its multidirectional asymptotic structure. Correlated radial-angular limits reveal directional curvature singularities that are invisible in the usual large-radius limit at fixed angle. We further exhibit causal geodesics that reach such singular asymptotic ends in finite affine parameter. Finally, we describe the maximally axial extension of this construction to higher dimensions: five dimensions are maximal for an entirely axial reduction to three dimensions, while six dimensions admit an additional nontrivial translational deformation, with further dimensions contributing only flat spectator directions.
CommentsA Mathematica notebook containing the doubly swirling Myers--Perry solution is available as an ancillary file in the arXiv source folder
