Gravitational correlation, black hole entropy and information conservation

TL;DR

This paper explores how gravitational correlations contribute to black hole entropy and demonstrates that entropy and information are conserved during Hawking radiation through gravitational correlation entropy analysis.

Contribution

It introduces the concept of gravitational correlation entropy to explain black hole entropy origin and shows entropy conservation during Hawking radiation.

Findings

Black hole entropy arises from interior gravitational correlations.

Entropy is conserved during Hawking radiation via gravitational correlations.

Unified description of black hole and ordinary matter entropy.

Abstract

When two objects have gravitational interaction between them, they are no longer independent of each other. In fact, there exists gravitational correlation between these two objects. Inspired by E. Verlinde's paper, we first calculate the entropy change of a system when gravity does positive work on this system. Based on the concept of gravitational correlation entropy, we prove that the entropy of a Schwarzschild black hole originates from the gravitational correlations between the interior matters of the black hole. By analyzing the gravitational correlation entropies in the process of Hawking radiation in a general context, we prove that the reduced entropy of a black hole is exactly carried away by the radiation and the gravitational correlations between these radiating particles, and the entropy or information is conserved at all times during Hawking radiation. Finally, we attempt to give a unified description of the non-extensive black-hole entropy and the extensive entropy of ordinary matter.