Classification of certain asymptotically AdS space-times with Ricci-flat boundary

TL;DR

This paper classifies specific solutions to Einstein's equations in asymptotically AdS space-times with Ricci-flat boundaries, revealing new solutions and their implications for boundary quantum field theories in non-equilibrium states.

Contribution

It introduces a classification of Einstein solutions with Ricci-flat boundary metrics and covariantly constant stress tensors, including new solutions relevant for holography.

Findings

New solutions to Einstein's equations in AdS with Ricci-flat boundary

Identification of solutions as null deformations of AdS or AdS soliton

Outline of scalar field coupling leading to non-Lorentz-invariant RG flows

Abstract

We classify solutions to Einstein's equations in AdS with Ricci-flat boundary metric and with covariantly constant boundary stress tensor, which in general is not diagonalizable, i.e. it does not admit a reference frame. New solutions are found, and in the context of the AdS/CFT duality they should describe a boundary QFT in certain non-equilibrium steady states. Further imposing the absence of scalar curvature singularities leads to a subset of metrics that can be seen as null deformations of AdS or of the AdS soliton. We also outline the procedure of solving the equations when a scalar is coupled to the metric, which holographically leads to non-Lorentz-invariant RG flows.