In order to prove the SRT one also needs to show that the connected components of the event horizon have the topology . This was established only recently by Chruściel and Wald [44], taking advantage of the topological censorship theorem [55]. A related version of the topology theorem, applying to globally hyperbolic – but not necessarily stationary – space-times was obtained by Jacobson and Venkataramani [103], and Galloway [56, 57, 58, 59]. We refer to [39], Sect. 2 for a detailed discussion.