Is entanglement entropy proportional to area?

TL;DR

This paper investigates whether entanglement entropy of a scalar field, including excited states, remains proportional to the area of a sphere, exploring its implications for black hole entropy and potential deviations from the area law.

Contribution

It extends previous work by analyzing the effects of excited states on the entanglement entropy-area proportionality.

Findings

Entanglement entropy remains approximately proportional to area even with excited states.

Deviations from the area law are observed when excited states are included.

Supports the idea that black hole entropy may originate from entanglement entropy.

Abstract

It is known that the entanglement entropy of a scalar field, found by tracing over its degrees of freedom inside a sphere of radius ${\cal R}$, is proportional to the area of the sphere (and not its volume). This suggests that the origin of black hole entropy, also proportional to its horizon area, may lie in the entanglement between the degrees of freedom inside and outside the horizon. We examine this proposal carefully by including excited states, to check probable deviations from the area law.