Riemannian light cone from vanishing birefringence in premetric vacuum electrodynamics

TL;DR

This paper shows that in premetric vacuum electrodynamics, vanishing birefringence leads to a Riemannian light cone, excluding Finslerian structures, and this result extends to dynamical equations of any order.

Contribution

It demonstrates that vanishing birefringence in premetric electrodynamics implies a Riemannian light cone, ruling out Finslerian geometries, and generalizes this to higher-order dynamical equations.

Findings

Vanishing birefringence implies a Riemannian light cone.

Finslerian structures cannot occur in this framework.

Results extend to dynamical equations of any order.

Abstract

We consider premetric electrodynamics with a local and linear constitutive law for the vacuum. Within this framework, we find quartic Fresnel wave surfaces for the propagation of light. If we require vanishing birefringence in vacuum, then a Riemannian light cone is implied. No proper Finslerian structure can occur. This is generalized to dynamical equations of any order.