Density matrix of radiation of black hole with fluctuating horizon

TL;DR

This paper calculates the density matrix of Hawking radiation for a black hole with a fluctuating horizon, revealing off-diagonal elements that encode correlations and potential information retention.

Contribution

It introduces a model incorporating quantum horizon fluctuations to modify the radiation density matrix, highlighting off-diagonal elements and their implications.

Findings

Off-diagonal elements encode correlations between radiation and black hole.

Quantum fluctuations smear the classical horizon, affecting the density matrix.

The smeared density matrix suggests possible information retention in Hawking radiation.

Abstract

The density matrix of Hawking radiation is calculated in the model of black hole with fluctuating horizon. Quantum fluctuations smear the classical horizon of black hole and modify the density matrix of radiation producing the off-diagonal elements. The off-diagonal elements may store information of correlations between radiation and black hole. The smeared density matrix was constructed by convolution of the density matrix calculated with the instantaneous horizon with the Gaussian distribution over the instantaneous horizons. The distribution has the extremum at the classical radius of the black hole and the width of order of the Planck length. Calculations were performed in the model of black hole formed by the thin collapsing shell which follows a trajectory which is a solution of the matching equations connecting the interior and exterior geometries.