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

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{ś}ciel-Herzlich \cite{CH} and introduce, for this class of spin static vacua, some Lorentzian manifolds which are prohibited as null infinities.

preprint2012arXivOpen access
Oussama HijaziSebastián Montiel
math.DG
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Oussama HijaziSebastián Montiel

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