Hologram of a pure state (AdS) black hole

We extend the HKLL holographic smearing function methods to reconstruct local bulk operators in the background of a large AdS black hole formed by null matter collapse (a \\\\pure state\\\" black hole) from the underlying CFT which is undergoing a sudden quench. In particular we probe the near horizon and sub-horizon bulk locality in the leading semiclassical limit (infinite N), and then ultimately their non-perturbative departure from locality by finite N effects. We show that such effects arise due to restrictions imposed by a proper coarse-graining prescription needed to defi ne semiclassical bulk observables. Our results have important implications on the black hole information problem. (Work in progress) Bases on: http://arxiv.org/abs/1505.03895 w/ D. Sarkar.