Eletromagnectic Geometry

We show that Maxwell’s electromagnetism can be mapped into the Born-Infeld theory in a curved space-time which depends only on the electromagnetic field in a specific way. This map is valid for any value of the two lorentz invariants F and G confirming that we have included all possible solutions of Maxwell’s equations. Our result seems to show that for a source-free electromagnetic theory specifying the dynamics and the space-time structure can be viewed as a choice of representation to describe the physical system.