Anti-de Sitter no-hair, AdS/CFT and the brane-world

We study the asymptotic behavior of the bulk spacetimes with a negative cosmological constant in the context of the brane-world scenario. We show that. in a Euclidean bulk, or in a Lorentzian static bulk, some sequences of hypersurfaces with a positive Ricci scalar evolve to warped geometries such as anti-de Sitter spacetime. Based on the AdS/CFT correspondence, we discuss that the positivity of the Ricci scalar is related to the stability of CFT on the brane. In addition. the brane world is described from the holographic point of view. The asymptotic local structure of the conformal infinity is also investigated.