A classification of the effective metric in nonlinear electrodynamics

TL;DR

This paper classifies the possible effective metrics in certain nonlinear electrodynamics theories, showing only two types exist, each characterized by a scalar function related to the energy-momentum tensor and Segré classification.

Contribution

It introduces a classification of effective metrics in nonlinear electrodynamics based on the energy-momentum tensor and Segré classification, identifying only two possible forms.

Findings

Two types of effective metrics are possible in certain nonlinear electromagnetic theories.

Each effective metric form is determined by a single scalar function.

Comparison with Minkowski light cone in two examples illustrates differences.

Abstract

We show that only two types of effective metrics are possible in certain nonlinear electromagnetic theories. This is achieved by using the dependence of the effective metric on the energy-momentum tensor of the background along with the Segr\`e classification of the latter. Each of these forms is completely determined by single scalar function, which characterizes the light cone of the nonlinear theory. We compare this light cone with that of Minkowski in two examples.