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 Chrusciel 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.