GLOBAL STRUCTURE OF A BLACK-HOLE COSMOS AND ITS EXTREMES

We analyze the global structure of a family of Einstein-Maxwell soluti ons parametrized by mass, charge and cosmological constant. In a quali tative classification there are: (i) generic black-hole solutions, des cribing a Wheeler wormhole in a closed cosmos of spatial topology S2 x S1; (ii) generic naked-singularity solutions, describing a pair of 'p oint'' charges in a closed cosmos; (iii) extreme black-hole solutions, describing a pair of 'homed'' particles in an otherwise closed cosmos ; (iv) extreme naked-singularity solutions, in which a pair of point c harges forms and then evaporates, in a way which is not even weakly ce nsored; and (v) an ultra-extreme solution. We discuss the properties o f the solutions and of various coordinate systems, and compare with th e Kastor-Traschen multi-black-hole solutions.