Recently, it was shown that type D black holes, encompassed in the large Plebanśki–Demiański (PD) family, exhibit a wide class of algebraically general generalizations via the application of Ehlers and Harrison transformations. In this work, we first discuss some mathematical details behind the composition of such transformations, and next, we introduce a qualitative picture of the most general type I generalization of the PD family, dubbed “Enhanced Plebanśki–Demiański” spacetime. We provide the exact form of the solution in the original PD coordinates, obtained via the simultaneous action of an Ehlers and a Harrison transformation on the vacuum PD geometry. In order to make the physics more transparent, we explicitly construct a rotating and accelerating black hole which further has NUT parameter and electric charges, both of them entering, not only the event horizon, but the Rindler horizon as well. This solution is directly obtained in the “physical” coordinates recently proposed by Podolský and Vrátny. Finally, a pedagogical appendix is thoughtfully included, providing readers with a user-friendly step-by-step guide to the Ernst formalism, in an attempt to address and resolve various minor inconsistencies frequently appearing in the relevant literature.

最近，研究表明，包含在大型 Plebanśki-Demiański (PD) 系列中的 D 型黑洞通过应用埃勒斯 (Ehlers) 和哈里森 (Harrison) 变换表现出广泛的代数一般概括。在这项工作中，我们首先讨论此类变换的组成背后的一些数学细节，接下来，我们介绍 PD 系列最一般的 I 型推广的定性图景，称为“增强的 Plebanśki-Demiański”时空。我们提供了原始 PD 坐标中解的精确形式，该坐标通过 Ehlers 和 Harrison 变换对真空 PD 几何结构的同时作用而获得。为了使物理更加透明，我们明确地构造了一个旋转和加速的黑洞，该黑洞还具有NUT参数和电荷，它们不仅进入事件视界，还进入Rindler视界。该解是直接在 Podolský 和 Vrátny 最近提出的“物理”坐标中获得的。最后，还精心包含了教学附录，为读者提供了用户友好的恩斯特形式主义分步指南，试图解决和解决相关文献中经常出现的各种细微的不一致之处。