We review the Debye potentials formalism for an electromagnetic test field on a fixed vacuum type D background and extend it in two different directions. (a) We show how to introduce sources (electric currents and charge distributions) in the framework of the Debye potentials. For the derivation all the three distinct possible Debye potentials are necessary but, fortunately, the fields outside the sources can still be described by a single Debye potential. (b) We present a new class of solutions (within the framework of the Debye potentials) which have been overlooked for a long time. The Maxwell equations represent in fact 3rd order partial differential equations for the Debye potentials. The known equations for the Debye potentials represent only a sufficient condition for the existence of source-free Maxwell field. This is exactly where the new solutions are “hidden”. Moreover, we found a completely new exact solution which describes physical process of charging of the black hole by charges infalling onto it along north and south axis at the speed of light. Finally, we seek for possible connections between the Debye potentials and the recently found Lunin potential. We also provide physical interpretation of some explicit solutions obtained by the Lunin potential.

我们回顾了固定真空 D 型背景上电磁测试场的德拜势形式，并将其扩展到两个不同的方向。(a) 我们展示了如何在德拜势的框架中引入源（电流和电荷分布）。对于推导所有三个不同的可能德拜势是必要的，但幸运的是，源之外的场仍然可以用单个德拜势来描述。(b) 我们提出了一类新的解决方案（在德拜势的框架内），这些解决方案长期以来一直被忽视。麦克斯韦方程实际上代表了德拜势的三阶偏微分方程。已知的德拜势方程仅代表了无源麦克斯韦场存在的充分条件。这正是新解决方案“隐藏”的地方。此外，我们发现了一个全新的精确解，它描述了电荷以光速沿南北轴落入黑洞的物理过程。最后，我们寻找德拜电位和最近发现的 Lunin 电位之间的可能联系。我们还提供了由 Lunin 势获得的一些显式解的物理解释。