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

作者：Hijazi Oussama^*; Montiel Sebastian; Raulot Simon

来源：Annals of Global Analysis and Geometry, 2015, 47(2): 167-178.

DOI：10.1007/s10455-014-9441-1

• Static vacuum
• De Sitter spacetime
• Killing horizon
• Dirac operator

We prove that, among all -dimensional spin static vacua with positive cosmological constant, the de Sitter spacetime is characterized by the fact that its spatial Killing horizons 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 -sphere. This extends uniqueness theorems shown in Boucher et al. (Phys Rev D 30:2447, 1984). ChruA > ciel [2]. to more general horizon metrics and to the non-single horizon case.

• 出版日期2015-2