No Holography for Eternal AdS Black Holes

It is generally believed that the eternal AdS black hole is dual to two conformal field theories with compact spatial sections that are together in a thermofield double state. We argue that this proposal is incorrect, and by extension so are the "entanglement=geometry" proposal of Van Raamsdonk and "ER=EPR" proposal of Maldacena and Susskind. We show that in the bulk there is an interaction needed between the two halves of the Hilbert space for connectivity across the horizon; however, there is no such interaction between the CFTs. This rules out the possibility of the dual to the CFTs being the eternal AdS black hole. We argue the correct dual "geometries" resemble the exterior of the black hole outside the stretched horizon but cap off before the global horizon. This disallows the possibility of a shared future (and past) wedge where Alice falling from one side can meet Bob falling from the other. We expect that in the UV complete theory the aforementioned caps will be fuzzballs.