Interacting Kerr-Newman electromagnetic fields

In this paper, we study some of the properties of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>G</a:mi><a:mo stretchy="false">→</a:mo><a:mn>0</a:mn></a:math> limit of the Kerr-Newman solution of Einstein-Maxwell equations. Carter noted the near equality between the gyromagnetic ratio, or g-factor, of the Kerr-Newman solution and of the electron. This observation is a consequence of the multipole structure of the Kerr-Newman field. We discuss additional coincidences between the Kerr-Newman multipole structure and the 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. Published by the American Physical Society 2024