2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35815In recent years there has been some progress in the understanding of the global structure of stationary black hole space-times. In this paper we review some new results concerning the structure of stationary black hole space-times. In particular we prove a corrected version of the ``black hole rigidity theorem'', and we prove a uniqueness theorem for static black holes with degenerate connected horizons. This paper is an expanded version of a lecture given at the Journées relativistes in Ascona, May 1996.24 pages, latex with amsfontsGeneral Relativity and Quantum Cosmologytext