论文标题
点粒子和Appell在Kerr Black Hole轴上的解决方案，以Debye电位为单位
Point particles and Appell's solutions on the axis of Kerr black hole for arbitrary spin in terms of the Debye potentials
论文作者
论文摘要
Teukolsky Master方程是D型空间中任何自旋或扰动的测试场的基本方程式 - 经典地以其分离形式对其进行了经典处理。然后，以串联的方式表示，即使代表最简单来源的解决方案 - 点粒子。唯一已知的例外是Schwarzschild黑洞附近的静态粒子（电荷或质量）。在这里，我们将此结果概括为Kerr Black Hole轴上任意自旋的静态点粒子。 Debye电位的简单代数公式可以明确地写下所考虑的田地的所有NP组件。后来，我们专注于电磁场，并采用经典的Appell的技巧（将源转移到一个复杂的空间中），以在Kerr背景上获得所谓的电磁魔术场。因此，获得了非平凡扩展但空间界限的场。我们还表明，在Kerr黑洞上方的静电点电荷引起了诱导，除了预期的电动单极，也是黑洞本身上的磁性单极电荷。这项贡献必须得到补偿。从一般层面上，我们就Debye的潜力讨论Teukolsky-Starobinsky的身份。
The Teukolsky master equation -- a fundamental equation for test fields of any spin, or perturbations, in type D spacetimes -- is classically treated in its separated form. Then the solutions representing even the simplest sources -- point particles -- are expressed in terms of series. The only known exception is a static particle (charge or mass) in the vicinity of Schwarzschild black hole. Here, we present a generalization of this result to a static point particle of arbitrary spin at the axis of Kerr black hole. A simple algebraic formula for the Debye potential from which all the NP components of the field under consideration can be generated is written down explicitly. Later, we focus on the electromagnetic field and employ the classic Appell's trick (moving the source into a complex space) to get so called electromagnetic magic field on the Kerr background. Thus the field of nontrivial extended yet spatially bounded source is obtained. We also show that a static electric point charge above the Kerr black hole induces, except an expected electric monopole, also a magnetic monopole charge on the black hole itself. This contribution has to be compensated. On a general level we discuss Teukolsky-Starobinsky identities in terms of the Debye potentials.
