Interacting Kerr-Newman Electromagnetic Fields

Abstract

In this paper, we study some of the properties of the $G \to 0$ limit of the Kerr-Newman solution of Einstein-Maxwell equations. Noting Carter's observation of the near equality between the $g = 2$ gyromagnetic ratio in the Kerr-Newman solution and that of the electron, we discuss additional such coincidences relating to the Kerr-Newman multipoles and properties of the electron. In contrast to the Coulomb field, this spinning Maxwell field has a finite Lagrangian. Moreover, by evaluating the Lagrangian for the superposition of two such Kerr-Newman electromagnetic fields on a flat background, we are able to find their interaction potential. This yields a correction to the Coulomb interaction due to the spin of the field.