论文标题
关于陶布纳特和克尔空间的Kähler结构
On Kähler Structures of Taub-NUT and Kerr Spaces
论文作者
论文摘要
在本文中，我们研究了Taub-nut和Kerr空间的Kählerian性质，它们是重力插入和黑洞溶液的一般相对论。我们表明，通过使用替代的显式coframe，相对于通常几乎复杂的结构，Euclidean Taub-nut公制是超级Kähler，而Euclidean Kerr Metric在全球范围内是kähler。我们还表明，通过应用原始度量标准的Lee形式或来自Weyl Tensor $（W^+）$的自偶会的因子，构成了kähler结构，可以通过施加的共形尺度缩放因子（w^+）$产生的子宫形式来接受Kähler结构。
In this paper, we study the Kählerian nature of Taub-NUT and Kerr spaces which are gravitational instanton and black hole solutions in general relativity. We show that Euclidean Taub-NUT metric is hyper-Kähler with respect to the usual almost complex structures by employing an alternative explicit coframe, and Euclidean Kerr metric is globally conformally Kähler. We also show that conformally scaled Euclidean Kerr space admits a Kähler structure by applying a conformal scaling factor stemming from the Lee-form of the original metric or alternatively a factor coming from self-dual part of the Weyl tensor $(W^+)$.
