Republication of: Black hole equilibrium states

This is a reprinting of Part 1 of Brandon Carter’s lectures given at the 1972 Les Houches school on black holes, first published in a book of proceedings of that school in 1973. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. The main value of this article is a comprehensive discussion of global properties of the Kerr solution, its maximal extension, its derivation from the separability of the Klein-Gordon equation and, most notably, its generalisation to nonzero cosmological constant. Numerous typos of the original text are corrected in this reprinting. The reprinted article is accompanied by an editorial note written by Niky Kamran and Andrzej Krasiński, and by B. Carter’s brief autobiography.