On the reconstruction of Lifshitz spacetimes

We consider the reconstruction of a lifshitz spacetime from three perspectives: differential entropy (or ‘hole-ography’), causal wedges and entanglement wedges. we find that not all time-varying bulk curves in vacuum lifshitz can be reconstructed via the differential entropy approach, adding a caveat to the general analysis of [1]. we show that the causal wedge for lifshitz spacetimes degenerates, while the entanglement wedge requires the additional consideration of a set of boundary-emanating light-sheets. the need to include bulk surfaces with no clear field theory interpretation in the differential entropy construction and the change in the entanglement wedge formation both serve as warnings against a naive application of holographic entanglement entropy proposals in lifshitz spacetimes.