Information and Coarse-Graining in Eternal Black Holes

Recently it was shown in the context of the AdS/CFT correspondence that the classical gravity description inevitably involves coarse-graining of some degrees. In this note we clarify the nature of this coarse-graining both in gravity and field theory sides. We show that the information carried by the bulk classical gravity fluctuation is transferred to the coarse-grained nonclassical degrees through tiny interactions, which makes the recovery of information almost impossible. Of course, the total system is evolving unitarily fully preserving its information as dictated by the basic construct of the AdS/CFT correspondence.