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Uniqueness of the AdS spacetime among static vacua with prescribed null infinity. (English) Zbl 1309.83014

Summary: 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.

MSC:

83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
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