Debye superpotential for charged rings or circular currents around Kerr black holes

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's function of the Teukolsky Master Equation (TME). The Debye potential itself is then, for a particular configuration, calculated in the same manner as the ${\ensuremath{\varphi}}_{0}$ field component is calculated from the Green's function of the TME---by convolution of the Green's 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.