Global dynamics of asymptotically locally AdS spacetimes with negative mass

TL;DR

This paper investigates the evolution of five-dimensional asymptotically locally AdS spacetimes with negative mass, showing that certain initial conditions lead to no horizon formation and potential naked singularities.

Contribution

It demonstrates that negative mass Eguchi-Hanson type initial data in biaxial Bianchi IX symmetry do not develop horizons, highlighting the possibility of naked singularities in such spacetimes.

Findings

Negative mass initial data do not form horizons.

Perturbations of Eguchi-Hanson-AdS cannot produce black holes.

Potential for naked singularities in these spacetimes.

Abstract

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.