Maxwell's theory on a post-Riemannian spacetime and the equivalence principle

TL;DR

This paper investigates how Maxwell's equations and the constitutive law are affected by torsion and nonmetricity in a post-Riemannian spacetime, showing that the equations remain unchanged but the constitutive relations may vary.

Contribution

It demonstrates that Maxwell's equations are invariant under extensions of spacetime geometry, with the constitutive law depending on additional geometric quantities like torsion and nonmetricity.

Findings

Maxwell's equations remain unchanged in post-Riemannian spacetime.

The constitutive law depends on metric, torsion, and nonmetricity.

Electric charge behavior analyzed in a specific gauge theory solution.

Abstract

The form of Maxwell's theory is well known in the framework of general relativity, a fact that is related to the applicability of the principle of equivalence to electromagnetic phenomena. We pose the question whether this form changes if torsion and/or nonmetricity fields are allowed for in spacetime. Starting from the conservation laws of electric charge and magnetic flux, we recognize that the Maxwell equations themselves remain the same, but the constitutive law must depend on the metric and, additionally, may depend on quantities related to torsion and/or nonmetricity. We illustrate our results by putting an electric charge on top of a spherically symmetric exact solution of the metric-affine gauge theory of gravity (comprising torsion and nonmetricity). All this is compared to the recent results of Vandyck.