  As demonstrated by Chernodub, vacuum in a strong magnetic field behaves as a
periodic Abrikosov vortex lattice in a type-II superconductor. We investigate
electromagnetic behavior of vacuum in this state. Since superconductivity is
realized along the axis of magnetic field only, strong anisotropy of the vacuum
dielectric tensor is observed. The diagonal components of the tensor are
positive in the x and y directions perpendicular to the magnetic field, and
negative in the z direction along the field. As a result, vacuum behaves as a
hyperbolic metamaterial medium. 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.
Spatial variations of the magnetic field curve this effective spacetime, and
may lead to formation of "event horizons", which are analogous to
electromagnetic black holes in hyperbolic metamaterials. We also note that
hyperbolic metamaterials behave as diffractionless "perfect lenses". Since
large enough magnetic fields probably had arisen in the course of evolution of
early Universe, the demonstrated hyperbolic behavior of early vacuum may have
imprints in the large scale structure of the present-day Universe.
