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Article Dans Une Revue Annals of Global Analysis and Geometry Année : 2015

Uniqueness of the de Sitter spacetime among static vacua with positive cosmological constant

Oussama Hijazi
Simon Raulot
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Résumé

We prove that, among all (n + 1)-dimensional spin static vacua with positive cosmological constant, the de Sitter spacetime is characterized by the fact that its spatial Killing hori-zons have minimal modes for the Dirac operator. As a consequence, the de Sitter spacetime is the only vacuum of this type for which the induced metric tensor on some of its Killing horizons is at least equal to that of a round (n − 1)-sphere. This extends unique-ness theorems shown by Boucher-Gibbons-Horowitz and Chruciel to more general horizon metrics and to the non-single horizon case.
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Dates et versions

hal-01116653 , version 1 (13-02-2015)

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Oussama Hijazi, Sebastian Montiel, Simon Raulot. Uniqueness of the de Sitter spacetime among static vacua with positive cosmological constant. Annals of Global Analysis and Geometry, 2015, 47 (2), pp.167-178. ⟨10.1007/s10455-014-9441-1⟩. ⟨hal-01116653⟩
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