## 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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