Could electromagnetism be envisaged as a form of gravity in a metric affine framework?

TL;DR

This paper explores the possibility that electromagnetism can be interpreted as a form of gravity within a metric-affine framework, revealing a gravito-electromagnetic equivalence through the homothetic curvature field.

Contribution

It demonstrates that a component of gravity, the homothetic curvature, satisfies Maxwell's equations, suggesting electromagnetism may be a manifestation of gravity in certain geometric frameworks.

Findings

Homothetic curvature satisfies Maxwell equations

Electromagnetism may be interpreted as a gravitational phenomenon

Raises questions about the nature of electromagnetism in curved spacetime

Abstract

We revisit the relativistic coupling between gravity and electromagnetism, putting particularly into question the status of the latter; whether it behaves as a source or as a form of gravity on large scales. Considering a metric-affine framework and a simple action principle, we find out that a component of gravity, the so-called homothetic curvature field, satisfies both sets of Maxwell equations. Therefore, we arrive at a gravito-electromagnetic equivalence analogous to the mass-energy equivalence. We raise and discuss some crucial questions implied by the aforementioned finding, refreshing our viewpoint of electromagnetism in curved spacetime.