Based on the work of Heemskerk, Marolf, Polchinski and Sully (HMPS), we study
the reconstruction of operators behind causal horizons in time dependent
geometries obtained by acting with shockwaves on pure states or thermal states.
These geometries admit a natural basis of gauge invariant operators, namely
those geodesically dressed to the boundary along geodesics which emanate from
the bifurcate horizon at constant Rindler time. We outline a procedure for
obtaining operators behind the causal horizon but inside the entanglement wedge
by exploiting the equality between bulk and boundary time evolution, as well as
the freedom to consider the operators evolved by distinct Hamiltonians. This
requires we carefully keep track of how the operators are gravitationally
dressed and that we address issues regarding background dependence. We compare
this procedure to reconstruction using modular flow, and illustrate some formal
points in simple cases such as AdS2 and AdS3.Comment: 48 pages, 14 figure
