ИСТИНА

The report considers modern Lorentz-invariant models of nonlinear vacuum electrodynamics inspired by the condition of regularization of the electromagnetic field energy, group symmetries and cosmological effects. Exact analytic solutions for compact astrophysical objects such as magnetic geons are discussed. The possibility of existence of a degenerate state of a charged black hole in the Einstein-Born-Infeld theory possessing a regular effective space-time for photons is observed.