用U（1）xU（1）等距对引力瞬子的棒结构分类
Rod-structure classification of gravitational instantons with U(1)xU(1) isometry
摘要：
杆结构形式在研究具有RxU（1）^{D-3}等距的D=4维和5维黑洞中起着重要的作用。在本文中，我们将这一理论应用于四维U（1）xU（1）等距的引力瞬子的研究，它可以作为五维黑洞的空间背景。我们首先介绍了一个更强的版本的棒结构与棒的方向适当规范化，并显示如何的正则性条件可以从它读出。要求没有圆锥形和orbifold奇点将在一般情况下施加周期性条件的坐标，我们说明了这一点，考虑已知的引力瞬子在这一类。在这个过程中，澄清了以前关于某些引力瞬子的一些结果。最后，我们展示了如何杆结构形式主义是能够提供一个分类的引力瞬子，并推测可能的新的引力瞬子的存在。
英文摘要：
The rod-structure formalism has played an important role in the study of black holes in D=4 and 5 dimensions with RxU(1)^{D-3} isometry. In this paper, we apply this formalism to the study of four-dimensional gravitational instantons with U(1)xU(1) isometry, which could serve as spatial backgrounds for five-dimensional black holes. We first introduce a stronger version of the rod structure with the rod directions appropriately normalised, and show how the regularity conditions can be read off from it. Requiring the absence of conical and orbifold singularities will in general impose periodicity conditions on the coordinates, and we illustrate this by considering known gravitational instantons in this class. Some previous results regarding certain gravitational instantons are clarified in the process. Finally, we show how the rod-structure formalism is able to provide a classification of gravitational instantons, and speculate on the existence of possible new gravitational instantons.
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