标题： D型黑洞再访：探讨其各种度规形式之间的关系 显示英文标题

标题： Black holes of type D revisited: relating their various metric forms

摘要： 我们研究了一类完整的时空，它们代表了带有旋转、NUT扭旋、加速、电荷和磁荷的黑洞。 这些是爱因斯坦-麦克斯韦方程的精确解，具有任意宇宙常数，其中（非零）电磁场与Weyl张量的双退化主零方向对齐。 特别是，我们明确地关联了这些解的各种坐标及其对应的物理参数，即原始的Plebański-Demiański (PD) 形式、最近发现且在此处形式上改进的方便的Astorino (A) 形式及其改进版(A+)、Griffiths-Podolsky (GP) 形式以及Podolsky-Vratný (PV) 形式的度规。 证明表明，如果正确映射并加以物理解释，所有这些表示都涵盖了完整的D类黑洞类别。 利用新的A参数，两个主要的PD四次度规函数被分解为二次表达式的乘积，从而可以进行显式分析。 此外，我们澄清了扭旋参数$\omega$的作用，它与Kerr-like旋转和NUT参数$a$和$l$分别相关。 特别关注加速NUT黑洞的神秘子类，其中包含$a=0$。 显示英文摘要

摘要： We investigate a complete family of spacetimes which represent black holes with rotation, NUT twist, acceleration, electric and magnetic charges. These are exact solutions of the Einstein-Maxwell equations with any cosmological constant, such that the (non-null) electromagnetic field is aligned with both the double-degenerate principal null directions of the Weyl tensor. In particular, we explicitly relate various coordinates and the corresponding physical parameters of such solutions, namely the original Plebanski-Demianski (PD) form, the convenient Astorino (A) form which was found recently, and formally improved here (A+), the Griffiths-Podolsky (GP), and Podolsky-Vratny (PV) form of the metric. It is demonstrated that, if properly mapped and physically interpreted, all these representations cover the complete class of type D black holes. Using the new A-parameters, the two main PD quartic metric functions are factorized into the product of quadratic expressions, enabling thus an explicit analysis. Moreover, we clarify the role of the twist parameter $\omega$, related to both the Kerr-like rotation and the NUT parameters $a$ and $l$, respectively. Special attention is payed to the elusive subclass of accelerating NUT black holes with $a=0$.