Uniqueness of the AdS spacetime among static vacua with prescribed null infinity

International audienceWe 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 byX.Wang [Wa2] and by Chruciel-Herzlich [CH] and introduce, for this class of spin static vacua, some Lorentzian manifolds which are prohibited as null infinities