On the uniqueness of the AdS space-time in higher dimensions

Abstract

In this paper, based on an intrinsic definition of asymptotically AdS space-times, we show that the standard anti-de Sitter space-time is the unique strictly stationary asymptotically AdS solution to the vacuum Einstein equations with negative cosmological constant in dimension less than 7. Instead of using the positive energy theorem for asymptotically hyperbolic spaces our approach appeals to the classic positive mass theorem for asymptotically flat spaces.

17 pages

References in corpus (4)

• Towards the classification of static vacuum spacetimes with negative cosmological constant
• Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature
• Positive Mass Theorem on Manifolds admitting Corners along a Hypersurface
• On the rigidity for conformally compact Einstein manifolds

Cited by in corpus (15)

• Mass rigidity for hyperbolic manifolds
• A no-go on strictly stationary spacetimes in four/higher dimensions
• On the mass of static metrics with positive cosmological constant - I
• Non-trivial, static, geodesically complete space-times with a negative cosmological constant II. $n\ge 5$
• Chemistry and Complexity for Solitons in AdS${}_5$
• Phase Transitions and Stability of Eguchi-Hanson-AdS Solitons
• Complex scalar field in strictly stationary Einstein-Maxwell-axion-dilaton spacetime with negative cosmological constant
• Brendle's inequality on static manifolds
• An infinity of black holes
• Deformations of Q-curvature II
• Monotonicity formulas for static metrics with non-zero cosmological constant
• Static Black Hole Uniqueness for nonpositive masses
• Static flow on complete noncompact manifolds I: short-time existence and asymptotic expansions at conformal infinity
• Ricci Curvature Rigidity for Weakly Asymptotically Hyperbolic Manifolds
• Brown-York mass and positive scalar curvature II - Besse's conjecture and related problems