Black Hole Entropy in Induced Gravity and Information Loss

TL;DR

This paper explores how black hole entropy can be understood through induced gravity, linking it to quantum correlations and information loss, especially in non-minimally coupled systems, offering a new perspective on the entropy's origin.

Contribution

It provides a novel interpretation of black hole entropy as quantum correlations in induced gravity, addressing limitations of previous entanglement entropy definitions.

Findings

Black hole entropy relates to quantum correlations between observable and non-observable states.

Non-minimal coupling causes the constituent energy to differ from the canonical Hamiltonian.

Previous entanglement entropy definitions failed to match Bekenstein-Hawking entropy.

Abstract

The basic assumption of the induced gravity approach is that Einstein theory is an effective, low energy-form of a quantum theory of constituents. In this approach the Bekenstein-Hawking entropy S^{BH} of a black hole can be interpreted as a measure of the loss of information about constituents inside the black hole horizon. To be more exact, S^{BH} is determined by quantum correlations between "observable" and "non-observable" states with positive and negative energy $\cal E$, respectively. It is important that for non-minimally coupled constituents $\cal E$ differs from the canonical Hamiltonian $\cal H$. This explains why previous definitions of the entanglement entropy in terms of $\cal H$ failed to reproduce S^{BH}.