Based on the work of Heemskerk, Marolf, Polchinski and Sully (HMPS), we studythe reconstruction of operators behind causal horizons in time dependentgeometries obtained by acting with shockwaves on pure states or thermal states.These geometries admit a natural basis of gauge invariant operators, namelythose geodesically dressed to the boundary along geodesics which emanate fromthe bifurcate horizon at constant Rindler time. We outline a procedure forobtaining operators behind the causal horizon but inside the entanglement wedgeby exploiting the equality between bulk and boundary time evolution, as well asthe freedom to consider the operators evolved by distinct Hamiltonians. Thisrequires we carefully keep track of how the operators are gravitationallydressed and that we address issues regarding background dependence. We comparethis procedure to reconstruction using modular flow, and illustrate some formalpoints in simple cases such as AdS$_2$ and AdS$_3$.
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