Abstract
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. Einstein's equations imply that at least one of the surfaces must be of constant curvature. It means that the symmetry of the metric arises as the consequence of the equations of motion (``spontaneous symmetry emergence''). Totally, we have 37 topologically different global solutions with spatial symmetry. There is one solution among them describing changing topology of space in time which is discussed in detail.
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