Canonical Purification of Evaporating Black Holes

Abstract

We show that the canonical purification of an evaporating black hole after the Page time consists of a short, connected, Lorentzian wormhole between two asymptotic boundaries, one of which is unitarily related to the radiation. This provides a quantitative and general realization of the predictions of ER=EPR in an evaporating black hole after the Page time; this further gives a standard AdS/CFT calculation of the entropy of the radiation (without modifications of the homology constraint). Before the Page time, the canonical purification consists of two disconnected, semiclassical black holes. From this, we construct two bipartite entangled holographic CFT states, with equal (and large) amount of entanglement, where the semiclassical dual of one has a connected ERB and the other does not. From this example, we speculate that measures of multipartite entanglement may offer a more complete picture into the emergence of spacetime.

43 pages, 12 figures. v2: fixed typos

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• Encoded information of mixed correlations: the views from one dimension higher
• Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity
• Boundary mutual information in double holography