Debye superpotential for charged rings or circular currents on Kerr black hole

TL;DR

This paper derives an explicit Debye superpotential for charged rings and circular currents on Kerr black holes, enabling exact calculations of electromagnetic fields in these complex spacetimes.

Contribution

It provides a closed-form expression for the Debye superpotential using the Green function of the Teukolsky Master Equation, advancing the analytical tools for electromagnetic fields on Kerr backgrounds.

Findings

Exact field of charged ring on Kerr obtained

Superpotential expressed explicitly and compactly

Method applicable to other circular source configurations

Abstract

We provide an explicit, closed and compact expression for the Debye superpotential of a circular source. This superpotential is obtained by integrating the Green function of Teukolsky Master Equation (TME). The Debye potential itself is then, for a particular configuration, calculated in the same manner as the $\phi_0$ field component is calculated from the Green function of the TME -- by convolution of the Green function with sources. This way we provide an exact field of charged ring and circular current on the Kerr background, finalizing thus the work of Linet.