On the nonlinear stability of higher-dimensional triaxial Bianchi IX black holes

In this paper, we prove that the 5-dimensional Schwarzschild-Tangherlini solution of the Einstein vacuum equations is orbitally stable (in the fully non-linear theory) with respect to vacuum perturbations of initial data preserving triaxial Bianchi IX symmetry. More generally, we prove that 5-dimensional vacuum spacetimes developing from suitable asymptotically flat triaxial Bianchi IX symmetric data and containing a trapped or marginally trapped homogeneous 3-surface 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.