Gravity in Warped Compactifications and the Holographic Stress Tensor

TL;DR

The paper analyzes gravity in warped brane-worlds using AdS/CFT to show that bulk Einstein equations with junction conditions induce full non-linear Einstein gravity on the brane, sourced by both brane matter and the holographic stress-energy tensor $\langle T_{ij} \rangle_{CFT}$. By combining Fefferman–Graham asymptotics for asymptotically AdS bulks with a local Gaussian-normal (near-brane) expansion, it derives higher-curvature corrections and an explicit effective Newton constant $G_4$ on the brane, valid for any bulk cosmological constant. In the asymptotically flat case, the analysis yields a brane cosmological term and a position-dependent Newton constant, tying the brane’s location to the effective gravity on the brane and illustrating gravity localization. Across both regimes, the results connect holographic renormalization, Brown–York stress-energy, and brane dynamics to provide a non-perturbative mechanism for 4D gravity emerging from higher-dimensional warped geometries.

Abstract

We study gravitational aspects of Brane-World scenarios. We show that the bulk Einstein equations together with the junction condition imply that the induced metric on the brane satisfies the full non-linear Einstein equations with a specific effective stress energy tensor. This result holds for any value of the bulk cosmological constant. The analysis is done by either placing the brane close to infinity or by considering the local geometry near the brane. In the case that the bulk spacetime is asymptotically AdS, we show that the effective stress energy tensor is equal to the sum of the stress energy tensor of matter localized on the brane and of the holographic stress energy tensor appearing in the AdS/CFT duality. In addition, there are specific higher-curvature corrections to Einstein's equations. We analyze in detail the case of asymptotically flat spacetime. We obtain asymptotic solutions of Einstein's equations and show that the effective Newton's constant on the brane depends on the position of the brane.