Global Structure of Spherically Symmetric Solutions of Einstein's Equations with an Electromagnetic Field

We classify all global spherically symmetric solutions of Einstein's equations with an electromagnetic field and a cosmological constant. The classification comprises 11 topologically inequivalent solutions. The spacetime is assumed to be a warped product of two surfaces. The study of global properties of solutions is carried out by the method of conformal blocks, which consists in analyzing the zeros and poles of a conformal factor contained in the spacetime metric.