Abstract

I will present a remarkable connection between solutions to vacuum Einstein gravity and to anti-de Sitter (AdS) gravity. More precisely, for every asymptotically anti–de Sitter (AdS) solution compactified on a torus there is a corresponding Ricci-flat solution obtained by replacing the torus by a sphere, performing a Weyl rescaling of the metric and appropriately analytically continuing the dimension of the torus/sphere. This operation maps Minkowski spacetime to AdS on a torus and AdS black branes to Schwarzschild black branes. When acting on the known solutions describing the hydrodynamic regime in AdS/CFT, it yields the stress tensor of asymptotically flat black branes to second order, which are constrained by the parent conformal symmetry. I will conclude with two simple applications of this correspondence: the analysis of the Gregory-Laflamme unstable modes of a black string, and the study the fluid dual to Rindler spacetime.