Gravity in Warped Compactifications and the Holographic Stress Tensor

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.