c © 2009 Birkhäuser Verlag Basel/Switzerland Annales Henri Poincaré Formation of Higher-dimensional Topological Black Holes

Abstract. We study higher dimensional gravitational collapse to topological black holes in two steps. Firstly, we construct some (n + 2)-dimensional collapsing space-times, which include generalised Lemâıtre-Tolman-Bondi-like solutions, and we prove that these can be matched to static Λ-vacuum exterior space-times. We then investigate the global properties of the matched solutions which, besides black holes, may include the existence of naked singularities and wormholes. Secondly, we consider as interiors classes of 5-dimensional collapsing solutions built on Riemannian Bianchi IX spatial metrics matched to radiating exteriors given by the Bizoń-Chmaj-Schmidt metric. In some cases, the data at the boundary for the exterior can be chosen to be close to the data for the Schwarzschild solution. 1