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On the nonlinear stability of higher dimensional triaxial Bianchi-IX black holes. (English) Zbl 1106.83014
The authors prove that the five-dimensional Schwarzschild–Tangherlini solution of the Einstein vacuum equations is orbitally stable with respect to vacuum perturbations of initial data preserving triaxial Bianchi-IX symmetry. The authors prove, that five-dimensional vacuum spacetimes developing from suitable asymptotically flat triaxial Bianchi-IX symmetric initial data and containing a trapped or marginally trapped homogeneous 3-surface necessarily possess a complete null infinity, whose past is bounded to the future by a regular event horizon, whose cross sectional volume in turn satisfies a Penrose inequality, relating it to the final Bondi mass. In particular, the results of this paper give the first examples of vacuum black holes which are not stationary exact solutions.
MSC:
83C57Black holes
83C20Classes of solutions of equations in general relativity
83E15Kaluza-Klein and other higher-dimensional theories