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

We construct a classification of dispersion relations for electromagnetic waves non-minimally coupled to space-time curvature, based on 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. (paper)