Classical electromagnetic potential as a part of gravitational connection: ideas and history

TL;DR

This paper revisits a lesser-known unified theory of gravity and electromagnetism from 1978, using a non-symmetric connection approach that naturally incorporates electromagnetic potential within gravitational geometry.

Contribution

It highlights a historical unification approach using metric and non-symmetric connection, proposing a more consistent matter inclusion and discussing future developments.

Findings

Reproduces Einstein-Maxwell equations with proper action choice

Identifies connection components with electromagnetic potential

Proposes improved matter coupling method

Abstract

We consider a natural form of unified theory of gravity and electromagnetism which was somehow missed at the time of intense search for such an unification, and was noticed only in 1978 but remained quite unknown. The basic idea of this unification is to use the metric and non-symmetric connection as independent variables, which generalizes the so-called Palatini formalism. The certain components of connection in the appearing theory can be naturally identified with electromagnetic potential, and with the proper choice of action the Einstein-Maxwell equations are reproducing. In this paper we compare such an approach with the known ideas of unification. Also we propose the more consistent way of including matter (in the form of classical particles) in the theory and briefly discuss the perspectives of further development of this approach.