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

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.