Non-minimal Einstein-Maxwell theory: the Fresnel equation and the Petrov classification of a trace-free susceptibility tensor

TL;DR

This paper classifies electromagnetic wave dispersion relations in non-minimal Einstein-Maxwell theory using the Petrov scheme, analyzing the Fresnel equation and wave surfaces based on a trace-free susceptibility tensor.

Contribution

It introduces a Petrov classification of dispersion relations in non-minimal Einstein-Maxwell theory based on the susceptibility tensor's properties.

Findings

Classification of solutions for all Petrov types

Analysis of specific features of dispersion relations

Visualization of wave surfaces for different Petrov types

Abstract

We construct a classification of dispersion relations for the electromagnetic waves non-minimally coupled to the space-time curvature, based on the analysis of the susceptibility tensor, which appears in the non-minimal Einstein-Maxwell theory. We classify solutions to the Fresnel equation for the model with a trace-free non-minimal susceptibility tensor according to the Petrov scheme. For all Petrov types we discuss specific features of the dispersion relations and plot the corresponding wave surfaces.