On the reconstruction of Lifshitz spacetimes

Understand

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 \cite{Headrick:2014eia}.
• 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.