Spacetime metric from linear electrodynamics II

TL;DR

This paper derives the conformally invariant part of spacetime metric from linear electrodynamics by formulating Maxwell's equations independently of the metric and analyzing the constitutive tensor and duality operator.

Contribution

It introduces a method to extract the conformal metric component from linear electrodynamics using a duality operator and axion field decomposition.

Findings

Derived the conformally invariant metric component from electrodynamics.

Established a duality operator based on the constitutive tensor.

Connected the axion field to spacetime metric properties.

Abstract

Following Kottler, \'E.Cartan, and van Dantzig, we formulate the Maxwell equations in a metric independent form in terms of the field strength $F=(E,B)$ and the excitation $H=({\cal D}, {\cal H})$. We assume a linear constitutive law between $H$ and $F$. First we split off a pseudo-scalar (axion) field from the constitutive tensor; its remaining 20 components can be used to define a duality operator $^#$ for 2-forms. If we enforce the constraint $^{##}=-1$, then we can derive of that the conformally invariant part of the {\em metric} of spacetime.