Einstein's unified field theory predicts the equilibrium positions of n wires run by steady electric currents

TL;DR

This paper demonstrates that Einstein's Hermitian theory of relativity can predict the equilibrium positions of multiple steady electric current-carrying wires, aligning with Maxwell's electrodynamics in the weak field limit.

Contribution

It provides an exact solution within Einstein's Hermitian theory that models the equilibrium of wires with currents, extending the theory's applicability to electromagnetic phenomena.

Findings

The solution describes n parallel wires at rest with steady currents.

Equilibrium positions are determined by cylindrical symmetry of the metric.

Results agree with Maxwell's electrodynamics in the weak field limit.

Abstract

A particular exact solution of Einstein's Hermitian theory of relativity is examined, after recalling that there is merit in adding phenomenological sources to the theory, and in choosing the metric like it was done long ago by Kursunoglu and Hely. It is shown by intrinsic arguments, relying on the properties of the chosen metric manifold, that the solution describes in Einstein's theory the field of n thin parallel wires at rest, run by steady electric currents, and predicts their equilibrium positions through the injunction that the metric must display cylindrical symmetry in the infinitesimal neighbourhood of each wire. In the weak field limit the equilibrium positions coincide with the ones prescribed by Maxwell's electrodynamics.