On the electromagnetic constitutive laws that are equivalent to spacetime metrics

TL;DR

This paper explores how electromagnetic constitutive laws derived from spacetime metrics relate to dielectric and magnetic properties, clarifying their mathematical equivalence and discussing their connection to effective metrics beyond the Gordon metric.

Contribution

It clarifies the equivalence between electromagnetic constitutive laws and spacetime metrics, and discusses the nature of dielectric and magnetic tensors derived from these metrics.

Findings

Electromagnetic constitutive laws can be represented by spacetime metrics.

The dielectric and magnetic tensors are directly related to the metric components.

Effective metrics generalize the Gordon metric in describing electromagnetic phenomena.

Abstract

The raising of both indices in the components of the Minkowski electromagnetic field strength 2-form to give the components of the electromagnetic excitation bivector field can be regarded as being equivalent to an electromagnetic constitutive law, as well as being defined by the components of the spacetime metric. This notion is clarified, and the nature of the equivalent dielectric tensors and magnetic permeability tensors that are defined by some common spacetime metrics is discussed. The relationship of the basic construction to effective metrics is discussed, and, in particular, the fact that this effective metric is more general than the Gordon metric.