  We consider general relativity with cosmological constant minimally coupled
to the electromagnetic field and assume that the four-dimensional space-time
manifold is a warped product of two surfaces with Lorentzian and Euclidean
signature metrics. Field equations imply that at least one of the surfaces must
be of constant curvature leading to the symmetry of the metric (``spontaneous
symmetry emergence''). We classify all global solutions in the case when the
Lorentzian surface is of constant curvature. These solutions are invariant with
respect to the Lorentz SO(1,2) or Poincare IO(1,1) groups acting on the
Lorentzian surface.
