Subregions, Minimal Surfaces, and Entropy in Semiclassical Gravity

TL;DR

This paper demonstrates that in semiclassical gravity, the entropy of a subregion is dominated by states minimizing boundary area, aligning with the Ryu-Takayanagi conjecture, and extends this to higher derivative gravity theories.

Contribution

It establishes a connection between reduced density matrices and minimal boundary surfaces in semiclassical gravity, including extensions to higher derivative theories.

Findings

Entropy is proportional to one quarter of the minimal boundary area.

The dominant states correspond to minimal boundary surfaces.

The framework extends to higher derivative gravity theories.

Abstract

For a large class of density matrices in semiclassical gravity, it is shown that the reduced density matrix which corresponds to tracing over the degrees of freedom in a spatial subregion is dominated by states for which the area of the boundary of the subregion is minimised. In the semiclassical limit, the entropy of the reduced density matrix is found to have a leading order contribution equal to one quarter of the minimal area in natural units. This is consistent with the Ryu-Takayanagi conjecture. An extension to higher derivative theories of gravity is established, for which the area is replaced by a dynamical generalisation of the Wald entropy.