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Point particles and Appell’s solutions on the axis of a Kerr black hole for an arbitrary spin in terms of the Debye potentials

Kofroň, David

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 ormass) in the vicinity ofa Schwarzschild black hole. Here, we present a generalization ofthis result to a static point particle of arbitrary spin at the axis ofa Kerr black hole. A simple algebraic formula for the Debye potential fromwhich all the Newman–Penrose components ofthe 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 the 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 for 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.
journal:Phys. Rev. D
grants:Thermodynamics of the gravitational field, GAČR 17-16260Y; 2017-2019; hlavní řešitel: Giovanni Acquaviva
kofro? - 2020 - point particles and appell's solutions on the axis of a kerr black hole for an arbitrary spin in terms of the debye pote.pdf (1501.22 kB)

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