Entanglement and entropy uncertainty in black hole quantum atmosphere

TL;DR

This paper explores how quantum entanglement and entropy uncertainty relate to Hawking radiation in black holes, revealing correlations that could shed light on the black hole information paradox and thermodynamics.

Contribution

It introduces a detailed analysis of entanglement and entropy uncertainty in black hole quantum atmospheres, highlighting their correlation with Hawking radiation and information distribution.

Findings

Entanglement characteristics peak at Hawking radiation maximum.

Opposite correlation between entanglement and entropy uncertainty.

Influence of black hole parameters on entropy uncertainty.

Abstract

In this work, we investigate the properties of Hawking radiation induced by the quantum atmosphere beyond the event horizon, by considering two detectors in Schwarzschild spacetime with the parameterized Hartle-Hawking temperature. \textcolor{black}{We explicitly study the dynamics of quantum entanglement and found that its characteristics are closely correlated with Hawking quantum radiation beyond the event horizon. Namely, its minimal value corresponds to the peak of Hawking radiation.} By virtue of the mutual information, we demonstrate the complementary relationship of the information distribution in the black hole. In addition, we detailedly discuss the influence of distance from the center of black hole to particle, radius of event horizon and Hartle-Hawking constant on the entropy uncertainty in the current scenario, and the results interestingly show that there exists an opposite correlation between the entanglement and the entropy uncertainty. It is believed that our observation could provide a new perspective for understanding the black hole information paradox and black hole thermodynamics.