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

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.