Canonical Purification of Evaporating Black Holes

TL;DR

This paper demonstrates that the canonical purification of an evaporating black hole after the Page time involves a connected wormhole, providing a concrete realization of ER=EPR and insights into spacetime emergence from entanglement.

Contribution

It offers a quantitative holographic model of black hole purification post-Page time, connecting entanglement structure with spacetime geometry, and constructs bipartite states illustrating different entanglement geometries.

Findings

Connected wormhole after Page time matches ER=EPR predictions

Pre-Page time purification consists of disconnected black holes

Entanglement measures may reveal spacetime emergence mechanisms

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.