Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1

TL;DR

The paper argues that the entropy of (near) extremal black holes is naturally interpreted as entanglement entropy of two entangled conformal quantum mechanics on the two AdS2 boundaries. It provides multiple concrete realizations: BTZ black holes via AdS3/CFT2, and near-extremal 5D black holes yielding an AdS2/CFT1 description with a DLCQ structure, where entanglement between two CQMs reproduces the Bekenstein-Hawking entropy, including higher-derivative corrections. To ground the proposal, the authors compute the entanglement entropy analytically in a finite-size, finite-temperature 2D CFT of a free Dirac fermion and show consistency with thermal entropy in the appropriate limit, thereby linking entanglement and thermal entropies holographically. The work thus strengthens the AdS2/CFT1 correspondence as a framework for microscopic black hole entropy and illuminates how holographic entanglement entropy operates in low dimensions, with implications for flat-space holography and future quantum gravity insights.

Abstract

We point out that the entropy of (near) extremal black holes can be interpreted as the entanglement entropy of dual conformal quantum mechanics via AdS2/CFT1. As an explicit example, we study near extremal BTZ black holes and derive this claim from AdS3/CFT2. We also analytically compute the entanglement entropy in the two dimensional CFT of a free Dirac fermion compactified on a circle at finite temperature. From this result, we clarify the relation between the thermal entropy and entanglement entropy, which is essential for the entanglement interpretation of black hole entropy.

Figures (7)

• Figure 1: Holographic picture of the entanglement entropy. (a) The length of the geodesic ${\gamma}_A$ whose boundary coincides with $\partial A$ gives the holographic entanglement entropy of the region $A$. (b) The region $A$ covers almost all the boundary as the length of the region $A$ gets large. (c) The disconnected curves with the same boundary as the one of (b), gives another candidate of ${\gamma}_A$. This consists of a part of black hole horizon and the geodesic extending to the boundary. The former has a finite length, while the latter is infinitely long $\sim {c\over 3}\log ({\epsilon}/a)$.
• Figure 2: The calculation of reduced density matrix $\rho_1$
• Figure 3: The geometry of AdS$_2$ [Left] and the 2D spacetime which is dual to the computation Tr$(\rho_1)^n$ [Right].
• Figure 4: Penrose diagrams of the extremal and non-extremal BTZ black hole. There is a closed timelike curve in the shaded region.
• Figure 5: The entanglement entropy as a function of $L$ when $\beta=0.6$. We get rid of the divergence due to the cut off by setting $a={1\over 2\pi}$.