Entanglement entropy of the black hole horizon

TL;DR

This paper explores the idea that black hole horizon entropy can be explained as entanglement entropy between the outside and a Planck-scale region inside the horizon, providing a potential explanation for Bekenstein-Hawking entropy.

Contribution

It introduces models in Minkowski and Rindler spacetime to calculate horizon entanglement entropy, linking it to black hole entropy without matter field corrections.

Findings

Entanglement entropy can account for Bekenstein-Hawking entropy.

Symmetry of entanglement entropy simplifies calculations.

Models demonstrate the entropy originates from quantum entanglement across the horizon.

Abstract

We examine a possibility that, when a black hole is formed, the information on the collapsed star is stored as the entanglement entropy between the outside and the thin region (of the order of the Planck length) of the inside the horizon. For this reason, we call this as the entanglement entropy of the black hole ``horizon''. We construct two models, one is in the Minkowski spacetime and the other is in the Rindler wedge. To calculate the entropy explicitly, we assume that the thin regions of the order of the Planck length of the outside and inside the horizon are completely entangled by quantum effects. We also use a property of the entanglement entropy that it is symmetric under an interchange of the observed and unobserved subsystems. Our setting and this symmetric property substantially reduce the needed numerical calculation. As a result of our analysis, we can explain the Bekenstein-Hawking entropy itself (rather than its correction by matter fields) in the context of the entanglement entropy.