The holographic map of an evaporating black hole

Abstract

We construct a holographic map that takes the semi-classical state of an evaporating black hole and its Hawking radiation to a microscopic model that reflects the scrambling dynamics of the black hole. The microscopic model is given by a nested sequence of random unitaries, each one implementing a scrambling time step of the black hole evolution. Differently from other models, energy conservation and the thermal nature of the Hawking radiation are taken into account. We show that the QES formula follows for the entropy of multiple subsets of the radiation and black hole. We further show that a version of entanglement wedge reconstruction can be proved by computing suitable trace norms and quantum fidelities involving the action of a unitary on a subset of Hawking partners. If the Hawking partner is in an island, its unitary can be reconstructed by a unitary on the radiation. We also adopt a similar setup and analyse reconstruction of unitaries acting on an infalling system.

Black hole complementarity from microstate models: a study of information replication and the encoding in the black hole interior

“…If we understand which specific information of subspaces of the residual infalling quantum matter (which retains information of its own initial state in the unitary mean field approximation) is encoded into specific portions of the interior undergoing ringdown, then we can study the detailed encoding into Hawking radiation by finding out which subregions of the bath has entanglement wedges (islands) overlapping with the same portions in the interior which is encoding the infalling information. In this regard, the recent works [51,52] are relevant.…”