Aspects of asymptotic electromagnetic fields

Abstract

The purpose of this paper is to develop the theory of asymptotic electromagnetic fields as presented in the classical paper by Goldberg and Kerr ( J. Math. Phys. 5 (1964), 172) in terms of retarded moments of the source 4-current involving integrals over null hyperplanes. The aspects of asymptotic electromagnetic fields which we discuss in some detail are: (i) the geometric optics approximation, (ii) the multipole expansion of the 4-potential, (iii) the arbitrary dependence of the electromagnetic field on a null coordinate, (iv) the comparison between the Goldberg-Kerr approach and the construction of asymptotic electromagnetic fields using sources defined with the aid of derivatives of Dirac delta functions, and (v) the two degrees of freedom of polarisation of the asymptotic electromagnetic field. Some of these topics are studied with a source having only retarded pole and dipole moments or having only retarded pole, dipole, and quadrupole moments. This is purely for the purpose of keeping the calculations within reasonable bounds. The extension of such calculations to sources possessing retarded multipole moments of higher orders will in most cases be obvious.