On the uniqueness of AdS space-time in higher dimensions

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 or equal to 8. Instead of using the positive energy theorem for asymptotically hyperbolic spaces with spin our approach appeals to the classic positive mass theorem for asymptotically flat spaces.