Black Hole Collisions, Analytic Continuation, and Cosmic Censorship

Abstract

Exact solutions of the Einstein-Maxwell equations that describe moving black holes in a cosmological setting are discussed with the aim of discovering the global structure and testing cosmic censorship. Continuation beyond the horizons present in these solutions is necessary in order to identify the global structure. Therefore the possibilities and methods of analytic extension of geometries are briefly reviewed. The global structure of the Reissner-Nordstr\"om-de Sitter geometry is found by these methods. When several black holes are present, the exact solution is no longer everywhere analytic, but less smooth extensions satisfying the Einstein equations everywhere are possible. Some of these provide counterexamples to cosmic censorship.