Formation of Higher-dimensional Topological Black Holes

We study higher-dimensional gravitational collapse to topological black holes in two steps. First, we construct some (n + 2)-dimensional collapsing space–times, which include generalised Lemaître–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. Second, 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.