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

TL;DR

This work investigates the asymptotic behavior of five-dimensional AdS bulks in brane-world scenarios and its holographic interpretation. By analyzing geodesic foliations and the effective brane equations, it shows that bulk geometries tend to AdS-like warpings under $R\ge 0$, while conformal infinity remains locally AdS-like; the AdS/CFT framework yields trace-like relations linking bulk dynamics to brane matter and CFT effects. The results support a brane-world no-hair behavior under appropriate energy/Ricci conditions and illuminate how holographic corrections influence brane gravity and cosmology. These insights have implications for gravity localization, the hierarchy problem, and the cosmological constant problem in AdS brane-worlds.

Abstract

We study the asymptotic behavior of the bulk spacetimes with the negative cosmological constant in the context of the brane-world scenario. We show that, in Euclidean bulk, or in Lorentzian static bulk, some sequences of hypersurfaces with the positive Ricci scalar evolve to the warped geometries like the 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.