Holographic entanglement entropy: near horizon geometry and disconnected regions

TL;DR

This paper investigates the behavior of holographic entanglement entropy for charged black holes and other geometries, focusing on near horizon effects, disconnected regions, and mutual information transitions in boundary theories.

Contribution

It analyzes the finite part of holographic entanglement entropy in various black hole backgrounds, including Lifshitz scaling, and explores mutual information transitions for multiple boundary regions.

Findings

Finite entanglement entropy scales with strip width.

Near horizon geometry determines divergent terms.

Mutual information transition depends on temperature and strip size.

Abstract

We study the finite term of the holographic entanglement entropy for the charged black hole in AdS(d+2) and other examples of black holes when the spatial region in the boundary theory is given by one or two parallel strips. For one large strip it scales like the width of the strip. The divergent term of its expansion as the turning point of the minimal surface approaches the horizon is determined by the near horizon geometry. Examples involving a Lifshitz scaling are also considered. For two equal strips in the boundary we study the transition of the mutual information given by the holographic prescription. In the case of the charged black hole, when the width of the strips becomes large this transition provides a characteristic finite distance depending on the temperature.