Advances in Theoretical and Mathematical Physics

Volume 18 (2014)

Number 1

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

Pages: 177 – 203

DOI: http://dx.doi.org/10.4310/ATMP.2014.v18.n1.a4

Authors

Oussama Hijazi (Institut Élie Cartan, Université de Lorraine Nancy, Vandoeuvre-lès-Nancy, France)

Sebastián Montiel (Departamento de Geometría y Topología, Universidad de Granada, Spain)

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 [40, 42] and by Chruściel-Herzlich [20] and introduce, for this class of spin static vacua, some Lorentzian manifolds which are prohibited as null infinities.

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