  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.
