  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.
