Hawking Radiation Correlations of Evaporating Black Holes in JT Gravity

TL;DR

This paper analyzes Hawking radiation correlations in evaporating black holes within JT gravity, revealing long-range correlations, entanglement structures, and limitations of semi-classical approximations, with implications for information recovery.

Contribution

It introduces a detailed analysis of radiation correlations, island saddle configurations, and entanglement bounds in evaporating black holes in JT gravity, highlighting new insights into information retrieval.

Findings

Hawking radiation exhibits long-range correlations.

Mutual information between early and late modes is significant.

Semi-classical approximation breaks down due to entropy inequality violations.

Abstract

We consider the Hawking radiation emitted by an evaporating black hole in JT gravity and compute the entropy of arbitrary subsets of the radiation in the slow evaporation limit, and find a zoo of possible island saddles. The Hawking radiation is shown to have long range correlations. We compute the mutual information between early and late modes and bound from below their squashed entanglement. A small subset of late modes are shown to be correlated with modes in a suitably large subset of the radiation previously emitted as well as later modes. We show how there is a breakdown of the semi-classical approximation in the form of a violation of the Araki-Lieb triangle entropy inequality, if the interior of the black hole and the radiation are considered to be separate systems. Finally, we consider how much of the radiation must be collected, and how early, to recover information thrown into the black hole as it evaporates.