The Holographic Map of an Evaporating Black Hole

TL;DR

This paper develops a detailed holographic model of an evaporating black hole, incorporating energy conservation and thermal radiation, and demonstrates how entanglement and reconstruction principles apply within this framework.

Contribution

It introduces a nested sequence of random unitaries model that accurately reflects black hole scrambling and supports entanglement wedge reconstruction with energy conservation.

Findings

QES formula verified for multiple radiation subsets

Entanglement wedge reconstruction demonstrated with trace norms and fidelities

Unitary reconstruction possible for Hawking partners in islands

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.