A geometric description of Maxwell field in a Kerr spacetime
Jacek Jezierski, Tomasz Smo{\l}ka
TL;DR
This paper introduces a geometric approach to describing Maxwell fields around Kerr black holes using a generalized Klein-Gordon equation derived from conformal Yano-Killing tensors, revealing unique properties of these tensors in Kerr spacetime.
Contribution
It proposes a novel geometric construction of the Fackerell-Ipser equation based on CYK tensors, advancing the understanding of electromagnetic fields in Kerr spacetime.
Findings
Derived a generalized Klein-Gordon equation for Maxwell fields in Kerr spacetime
Identified unique properties of CYK tensors relevant to electrodynamics
Provided a geometric framework for analyzing electromagnetic phenomena near black holes
Abstract
We consider the Maxwell field in the exterior of a Kerr black hole. For this system, we propose a geometric construction of generalized Klein-Gordon equation called Fackerell-Ipser equation. Our model is based on conformal Yano-Kiling tensor (CYK tensor). We present non-standard properties of CYK tensors in the Kerr spacetime which are useful in electrodynamics.
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