标题： 黑洞和引力瞬子的凯勒几何 显示英文标题

标题： Kaehler geometry of black holes and gravitational instantons

摘要： 我们得到了一个广义四维洛伦兹或欧几里得共形“凯勒”几何的凯勒势的闭合公式，包括Plebanski-Demianski类和各种引力瞬子，如Fubini-Study和Chen-Teo。 我们证明了施瓦茨希尔德和克尔的凯勒势通过纽曼-贾尼斯位移相关联。 我们的方法还表明，一类超引力黑洞，包括Kerr-Sen时空，是埃尔米特的（但不是共形凯勒的）。 最后，我们证明复结构的可积性条件自然导致（非线性）威兰双复制，并给出了这种关系的新真空和非真空例子。 显示英文摘要

摘要： We obtain a closed formula for the Kaehler potential of a broad class of four-dimensional Lorentzian or Euclidean conformal "Kaehler" geometries, including the Plebanski-Demianski class and various gravitational instantons such as Fubini-Study and Chen-Teo. We show that the Kaehler potentials of Schwarzschild and Kerr are related by a Newman-Janis shift. Our method also shows that a class of supergravity black holes, including the Kerr-Sen spacetime, is Hermitian (but not conformal Kaehler). We finally show that the integrability conditions of complex structures lead naturally to the (non-linear) Weyl double copy, and we give new vacuum and non-vacuum examples of this relation.