Entanglement entropy of black holes and AdS/CFT correspondence

TL;DR

The paper extends the Ryu–Takayanagi holographic entanglement entropy framework to black holes living on the boundary of AdS space, and validates the construction in both $d=2$ and $d=4$ boundary dimensions. It shows that entanglement entropy can be computed as the area of a minimal surface anchored to the black hole horizon and a boundary sphere, reproducing known UV-divergent structures and finite terms. In 4D, it uncovers a novel universal finite term that scales as $L_{inv}^{2}\ln L_{inv}$, controlled by the obstruction tensor at the horizon, and relates this to strongly coupled CFTs like $\mathcal{N}=4$ SYM. The work reinforces the interpretation of black hole entropy as entanglement entropy and provides concrete, testable predictions for holographic entanglement in higher dimensions.

Abstract

A recent proposal by Ryu and Takayanagi for a holographic interpretation of entanglement entropy in conformal field theories dual to supergravity on anti-de Sitter (adS) is generalized to include entanglement entropy of black holes living on the boundary of adS. The generalized proposal is verified in boundary dimensions $d=2$ and $d=4$ for both the UV divergent and UV finite terms. In dimension $d=4$ an expansion of entanglement entropy in terms of size $L$ of the subsystem outside the black hole is considered. A new term in the entropy of dual strongly coupled CFT, which universally grows as $L^2\ln L$ and is proportional to the value of the obstruction tensor at the black hole horizon, is predicted.