  The Einstein vacuum equations in five dimensions with negative cosmological
constant are studied in biaxial Bianchi IX symmetry. We show that if initial
data of Eguchi-Hanson type, modelled after the four-dimensional Riemannian
Eguchi-Hanson space, have negative mass, the future maximal development does
not contain horizons, i.e. the complement of the causal past of null infinity
is empty. In particular, perturbations of Eguchi-Hanson-AdS spacetimes within
the biaxial Bianchi IX symmetry class cannot form horizons, suggesting that
such spacetimes are potential candidates for a naked singularity to form. The
proof relies on an extension principle proven for this system and a priori
estimates following from the monotonicity of the Hawking mass.
