%0 Journal Article %T Uniqueness of smooth stationary black holes in vacuum: small perturbations of the Kerr spaces %A S. Alexakis %A A. D. Ionescu %A S. Klainerman %J Mathematics %D 2009 %I arXiv %R 10.1007/s00220-010-1072-1 %X We prove that a regular stationary black-hole solution of the Einstein vacuum equations which is "close" to some Kerr solution is, in fact, isometric to that Kerr solution. %U http://arxiv.org/abs/0904.0982v1