  A self-consistent extended Einstein-Maxwell model for relativistic
non-stationary polarizable-magnetizable anisotropic media is presented. Based
on the analogy with relativistic extended irreversible (transient)
thermodynamics, the extended constitutive equations for the electrodynamics of
continua are formulated phenomenologically, the convective derivatives of the
first, second, etc. orders being taken into account. The master equations for
the gravity field contain a modified effective (symmetric) stress-energy tensor
of the electromagnetic field in a material medium, the use of this tensor being
motivated both by historical analogies and direct variational procedure. By way
of example we consider the exact solution of the extended Einstein-Maxwell
model, describing the isotropic cosmological model with hidden non-vanishing
electromagnetic field, electric polarization and magnetization.
