Dafermos–Holzegel conjecture on naked singularity formation for Eguchi-Hanson-AdS perturbations

Let small perturbations of Eguchi-Hanson-AdS spacetimes be given, and let a Penrose diagram describe their global development. Let $\mathcal I$ denote null infinity.

Dafermos–Holzegel conjecture. Small perturbations of Eguchi-Hanson-AdS spacetimes have a Penrose diagram as depicted in Figure~. Moreover, $\mathcal I$ is future incomplete.

The paper's main theorem rules out future horizons for these perturbations, supporting the proposed naked-singularity diagram; the conjecture is not established in full, and the formation of a first singularity remains an open possibility.