A classification of the effective metric in nonlinear electrodynamics

Understand

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.