2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/177373We show that static electro--vacuum black hole space--times containing an asymptotically flat spacelike hypersurface with compact interior and with both degenerate and non--degenerate components of the event horizon do not exist. This is done by a careful study of the near-horizon geometry of degenerate horizons, which allows us to eliminate the last restriction of the static electro-vacuum no-hair theory.Latex2e, 14 pages in A4, minor corrections and improvements of the presentationGeneral Relativity and Quantum Cosmologytext