Density matrix of radiation of a black hole with a fluctuating horizon

The density matrix of Hawking radiation is calculated in the model of a black hole with a fluctuating horizon. Quantum fluctuations smear the classical horizon of a black hole and modify the density matrix of radiation producing the off-diagonal elements. The off-diagonal elements may store information on correlations between the radiation and the 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 a black hole formed by the thin collapsing shell which follows a trajectory that is a solution of the matching equations connecting the interior and exterior geometries.

Figure 1

Penrose diagram for the collapsing shell. For $u<0$, the shell is in phase I, for $u>0$, it is in phase II. $v_H$ is the point of horizon formation.