Global properties of Spherically symmetric solutions in General Relativity with an Electromagnetic field and a Cosmological constant

We consider general relativity with cosmological constant minimally coupled to electromagnetic field. We assume that four-dimensional space-time manifold is the 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. It is leading to the symmetry of the metric, although any symmetry of solutions is not assumed from the very beginning. This effect is called «spontaneous symmetry emergence». We have been obtained 11 global spherically symmetric solutions, among them there are well known solutions: Reissner-Nordstrom solution, extremal black hole and naked singularity. To construct Carter-Penrose diagrams, we use the conformal block method. There is a new global spherically symmetric solution, which describes changing topology of spatial sections during the time evolution at the classical level.