Black hole entropy as entanglement entropy: a holographic derivation

TL;DR

It is argued that a recent proposal for computing entanglement entropy using AdS/CFT holography implies that black hole entropy can be exactly equated with entanglements entropy.

Abstract

We study the possibility that black hole entropy be identified as entropy of entanglement across the horizon of the vacuum of a quantum field in the presence of the black hole. We argue that a recent proposal for computing entanglement entropy using AdS/CFT holography implies that black hole entropy can be exactly equated with entanglement entropy. The implementation of entanglement entropy in this context solves all the problems (such as cutoff dependence and the species problem) typically associated with this identification.

Figures (2)

• Figure 1: Conformal diagram of the spacetime for a black hole on a brane in AdS. On a spatial slice at constant time (shaded) the horizon of the black hole is a minimal surface.
• Figure 2: Minimal surface $\gamma$ computing the entanglement across a circle $C$ on a flat plane. A spatial section of AdS is represented as the Poincare upper-half-volume. The shaded region $0\leq z<R$ is cut off in the RS2 construction. The minimal surface is a hemisphere, of which only the portion above $z=R$ is relevant. The length of the circle $C$ is fixed to be $\mathcal{C}_{h}$. The proper distance along $z$ is $R\log(z/R)$, so when $R/\mathcal{C}_{h}\ll 1$ the hemisphere is actually pancaked along the brane.