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

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

2003-10-18

arxiv.org/abs/math/0310281v1

Annales Henri Poincare 5 (2004) 245-260

Mathematics

Differential Geometry

17 pages

Scientific paper

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.

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