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Formation of higher-dimensional topological black holes. (English) Zbl 1208.83071
Summary: 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.
MSC:
83C57Black holes
83E15Kaluza-Klein and other higher-dimensional theories
83C75Space-time singularities, cosmic censorship, etc.
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