Spacetime metric from linear electrodynamics

TL;DR

This paper derives the spacetime metric from linear electrodynamics by formulating Maxwell's equations on a general manifold and imposing a linear constitutive relation between electromagnetic fields and excitations.

Contribution

It introduces a method to determine the spacetime metric directly from electromagnetic properties using a linear constitutive relation.

Findings

Spacetime metric can be derived from electromagnetic constitutive relations.

Maxwell equations are formulated on an arbitrary manifold.

The approach links electromagnetic properties to spacetime geometry.

Abstract

The Maxwell equations are formulated on an arbitrary (1+3)-dimensional manifold. Then, imposing a (constrained) linear constitutive relation between electromagnetic field $(E,B)$ and excitation $({\cal D},{\cal H})$, we derive the metric of spacetime therefrom.