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 and by Chruściel-Herzlich and introduce, for this class of spin static vacua, some Lorentzian manifolds which are prohibited as null infinities.