Uniqueness of the AdS Spacetime among Static Vacua with prescribed Null infinity

TL;DR

This paper proves that among static vacuum spacetimes with negative cosmological constant, only the Anti-de Sitter (AdS) spacetime has a null infinity boundary admitting a non-trivial Killing spinor, establishing a uniqueness result.

Contribution

It generalizes previous uniqueness theorems for static vacua by characterizing AdS spacetime through spinor boundary conditions and introduces new restrictions on possible null infinities.

Findings

AdS spacetime uniquely characterized by boundary Killing spinors

Generalization of previous uniqueness results

Identification of prohibited null infinities for this class

Abstract

We prove that an $(n+1)$-dimensional spin static vacuum with negative cosmological constant whose null infinity has a boundary admitting a non-trivial Killing spinor field is the AdS spacetime. As a consequence, we generalize previous uniqueness results by X. Wang \cite{Wa2} and by Chru{\'s}ciel-Herzlich \cite{CH} and introduce, for this class of spin static vacua, some Lorentzian manifolds which are prohibited as null infinities.