Large D black holes in an environment

We construct dynamical black hole solutions to Einstein Equations in presence of matter in the large D limit. The matter stress tensors that we consider are weak in the sense that they source asymptotic spacetimes with internal curvatures of the order of O(D-0). Apart from this, we work with a generic stress tensor demanding only that the stress tensor satisfies the conservation equations. The black hole solutions are obtained in terms of the dual non-gravitational picture of membranes propagating in spacetimes equivalent to the asymptotes of the black holes. We obtain the metric solutions to the second sub-leading order in 1/D. We also obtain the equations governing the dual membranes up to the first sub-leading order in 1/D.