Interacting Kerr-Newman Electromagnetic Fields

TL;DR

This paper explores the properties of Kerr-Newman electromagnetic fields in the zero-gravity limit, revealing their unique multipole structures, finite Lagrangian, and spin-induced corrections to Coulomb interactions, with implications for electron-like particles.

Contribution

It introduces a novel analysis of Kerr-Newman electromagnetic fields' properties and interactions, highlighting their finite Lagrangian and spin effects on Coulomb potential.

Findings

Kerr-Newman fields have finite Lagrangian unlike Coulomb fields.

Superposition of two Kerr-Newman fields yields a spin-dependent interaction correction.

The gyromagnetic ratio of Kerr-Newman matches that of the electron.

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.