On multipole moments of the electromagnetic field (Q1898124)

In this paper, we compare two approaches to electromagnetic theory in flat space-time. Using the Newman-Penrose formalism, multipole moments of the electromagnetic field have been identified without determining their relation to the source of the field. Using the formalism developed by \textit{J. N. Goldberg} and \textit{R. P. Kerr} [J. Math. Phys. 5, 172-176 (1964; Zbl 0118.225)], we obtain this relation explicitly for an extended pole-dipole-quadrupole source. Our results extend in an obvious manner to more general sources; to keep the calculations to a reasonable size, we consider only this case. As a convenient check on calculations, we verify explicitly the vanishing of the Newman-Penrose constants associated with these electromagnetic fields. Our results add to the development of the Goldberg-Kerr formalism initiated by \textit{P. A. Hogan} and \textit{G. F. R. Ellis} [Ann. Phys. 210, No. 1, 178-237 (1991)].