Generalized Nordstr\"om Theory Revisited Part II: Nordstr\"om & Maxwell United

TL;DR

This paper revisits a unified theory combining gravitation and electromagnetism using a complex Randers metric, aligning with General Relativity's predictions and resolving previous issues with singularities and field dichotomies.

Contribution

It introduces a complex Randers metric framework that unifies gravity and electromagnetism, aligning with Einstein's vision and improving upon earlier models.

Findings

Theory's predictions agree with General Relativity to leading order.

Metric solutions are free of spurious singularities.

Unified stress-energy tensor includes gravitational and electromagnetic energy.

Abstract

In 1945 Einstein concluded that [1]: "The present theory of relativity is based on a division of physical reality into a metric field (gravitation) on the one hand, and into an electromagnetic field and matter on the other hand. In reality space will probably be of a uniform character and the present theory be valid only as a limiting case. For large densities of field and of matter, the field equations and even the field variables which enter into them will have no real significance.". The dichotomy is resolved by introducing a complex Randers metric with a real valued scalar field and complex valued vector field, providing a unified mathematical framework for gravitation & electromagnetism for which the resulting theory's predictions agree with General Relativity; to leading order in the gravitational constant. Hence, the related experimental results validate both theories; and the former theory's metric solutions are free of spurious singularities, because its stress-energy tensor includes the energy & momentum for the gravitational field; like e.g. Maxwell's stress-energy tensor contains the electromagnetic field.