发表机构
University of Amsterdam（阿姆斯特丹大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在五维共形不变类克尔翘曲黎曼膜世界流形上构造出含整数参数的精确引力瞬子解，利用对称性与纤维化方法推导，还证明其可变换为具凯勒势的自对偶凯勒流形。
AI 中文摘要
我们在五维共形不变类克尔翘曲黎曼膜世界流形上给出了一个精确的引力瞬子解，该几何可描述为凯勒流形$\boldsymbol{\times}\boldsymbol{\times}\boldsymbol{R}$。通过将$S^3$的二重覆盖经球极投影应用到有效四维流形的$\boldsymbol{\times}\boldsymbol{CP}^1$上，并结合克莱因曲面构造，我们利用了潜在的$\boldsymbol{Z}_2$对称性。该瞬子随后通过在对径$S^2$上纤维化得到，其度规由含整数参数的一阶微分方程确定，而描述角动量分量的方程与其余场方程解耦。最后，我们证明该解允许解析复变换为局域共形相关的凯勒流形，且该流形具有凯勒势，从而显式展现出自对偶结构。
英文摘要
We present an exact gravitational instanton solution on a five-dimensional, conformally invariant, Kerr-like warped Riemannian brane-world manifold. The geometry can be described as the Kähler manifold $\mathbb{C}^1\times\mathbb{C}^1\times \mathbb{R}$. By applying a double cover of $S^3$ through stereographic projection onto $\mathbb{C}P^1\times \mathbb{C}P^1$ of the effective four-dimensional manifold, together with the Klein surface construction, we exploit the underlying $\mathbb{Z}_2$ symmetry. The instanton is then obtained by fibering over the antipodal $S^2$. The metric is determined by a first-order differential equation containing an integer parameter, while the equation governing the angular momentum component decouples from the remaining field equations. Finally, we show that our solution admits an analytic complex transformation to a locally conformally related Kähler manifold possessing a Kähler potential, thereby making the self-dual structure manifest.
CommentsV2: Some minor corrections. Some figures added. Shorter version of previous submission. 23 pages and 4 figures
