Entanglement entropy of a scalar field across a spherical boundary in the Einstein universe

TL;DR

This paper investigates the entanglement entropy of a scalar field in an Einstein universe, demonstrating that it still follows an area law similar to flat space, despite the universe's curvature.

Contribution

It extends the understanding of entanglement entropy's area law to curved backgrounds, showing insensitivity to large-scale geometry in an Einstein universe.

Findings

Entanglement entropy scales linearly with the boundary area.

Curvature of the Einstein universe does not alter the area law.

Entropy primarily arises from degrees of freedom near the boundary.

Abstract

A scalar field in the ground state, when partially hidden from observation by a spherical boundary, acquires entanglement entropy $S$ proportional to the area of the surface. This area law is well established in flat space, where it follows almost directly from dimensional arguments. We study its validity in an Einstein universe, whose curvature provides an additional physical parameter on which the entropy could, in principle, depend. The surprisingly simple result is that the entanglement entropy still scales linearly with the area. This is supported by other observations to the effect that the entanglement entropy arises mostly from degrees of freedom near the boundary, making it insensitive to the large-scale geometry of the background space.