The Electrostatics of Einstein's Unified Field Theory

TL;DR

This paper explores the electrostatic solutions in Einstein's Hermitian theory, showing how a physically correct metric influences the structure and equilibrium of multiple charged particles.

Contribution

It demonstrates the electrostatic solutions within Einstein's Hermitian theory using Hély's metric, clarifying the structure and equilibrium conditions of charged particles.

Findings

Exact electrostatic solutions for n point charges in Einstein's Hermitian theory.

Spherical symmetry conditions yield electrostatic equilibrium.

Hély's metric correctly describes wave fronts and matter behavior.

Abstract

When sources are added at their right-hand sides, and g_{(ik)} is a priori assumed to be the metric, the equations of Einstein's Hermitian theory of relativity were shown to allow for an exact solution that describes the general electrostatic field of n point charges. Moreover, the injunction of spherical symmetry of g_{(ik)} in the infinitesimal neighbourhood of each of the charges was proved to yield the equilibrium conditions of the n charges in keeping with ordinary electrostatics. The tensor g_{(ik)}, however, cannot be the metric of the theory, since it enters neither the eikonal equation nor the equation of motion of uncharged test particles. A physically correct metric that rules both the behaviour of wave fronts and of uncharged matter is the one indicated by H\'ely. In the present paper it is shown how the electrostatic solution predicts the structure of the n charged particles and their mutual positions of electrostatic equilibrium when H\'ely's physically correct metric is adopted.