Vacuum in a Strong Magnetic Field as a Hyperbolic Metamaterial

As demonstrated by Chernodub, vacuum in a strong magnetic field behaves as Abrikosov vortex lattice in a type-II superconductor. We investigate electromagnetic behavior of vacuum in this state and demonstrate that vacuum behaves as a hyperbolic metamaterial. If the magnetic field is constant, low frequency extraordinary photons experience this medium as a (3 + 1) Minkowski spacetime in which the role of time is played by the spatial z coordinate. Variations of the magnetic field curve this spacetime, and may lead to formation of "electromagnetic black holes." Since hyperbolic metamaterials behave as diffractionless "perfect lenses," and large enough magnetic fields probably existed in the early Universe, the demonstrated hyperbolic behavior of early vacuum may have imprints in the large scale structure of the present-day Universe.