Uniqueness of the de Sitter spacetime among static vacua with positive cosmological constant
arXiv:1502.04090 · doi:10.1007/s10455-014-9441-1
Abstract
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.
arXiv commentin Annals of Global Analysis and Geometry, Springer Verlag (Germany), 2014
References in corpus (10)
- Bohm and Einstein-Sasaki Metrics, Black Holes and Cosmological Event Horizons
- A note on static spaces and related problems
- Towards the classification of static vacuum spacetimes with negative cosmological constant
- Towards a classification of static electro-vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior
- Scalar Curvature Rigidity for asymptotically locally hyperbolic manifolds
- The classification of static vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior
- On the structure of solutions to the static vacuum Einstein equations
- On stationary vacuum solutions to the Einstein equations
- On the Geometry and Mass of Static, Asymptotically AdS Spacetimes, and the Uniqueness of the AdS Soliton
- On the rigidity for conformally compact Einstein manifolds
Cited by in corpus (8)
- Remarks on critical metrics of the scalar curvature and volume functionals on compact manifolds with boundary
- On the mass of static metrics with positive cosmological constant - I
- Quantum reverse hypercontractivity: its tensorization and application to strong converses
- On the mass of static metrics with positive cosmological constant -- II
- On static three-manifolds with positive scalar curvature
- Monotonicity formulas for static metrics with non-zero cosmological constant
- Critical metrics of the volume functional on compact three-manifolds with smooth boundary
- Brown-York mass and positive scalar curvature II - Besse's conjecture and related problems