# Entanglement Entropy of AdS Black Holes

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## Abstract

**:**

## 1. Introduction

## 2. Review of Entanglement Entropy

#### 2.1. Entanglement in QFT

#### 2.2. Entanglement Entropy of a 2D CFT

**Figure 1.**The three different forms of the 2D spacetime. ϕ is the spacelike coordinate and t is the timelike one.

#### 2.3. AdS/CFT Correspondence and UV/IR Connection

#### 2.4. Entanglement Entropy of Black Holes

## 3. 2D AdS Black Holes

#### 3.1. Entanglement Entropy of the 2D Black Hole

- (1)
- Equation (5) holds for a 2D flat spacetime, whereas we are dealing with a curved 2D background.
- (2)
- The calculations leading to Equation (5) are performed for a spacelike slice Q, whereas in the black hole case there is no global notion of a spacelike coordinate, owing to the coordinate singularities at $r={r}_{h}$ (the location of the horizon) and at $r=\infty $ (the location of the timelike asymptotic boundary of the AdS spacetime).

#### 3.2. Large Black Hole Mass Behavior

## 4. BTZ Black Holes

#### 4.1. AdS${}_{3}$ Gravity and Dual CFT${}_{2}$

#### 4.2. Modular Invariance

#### 4.3. EE and the UV/IR Relation

#### 4.4. Holographic EE of Conical Singularities

#### 4.5. Holographic Entanglement Entropy of the BTZ Black Hole

#### 4.6. Entanglement Entropy vs. Thermal Entropy

## 5. Conclusions

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Cadoni, M.; Melis, M.
Entanglement Entropy of AdS Black Holes. *Entropy* **2010**, *12*, 2244-2267.
https://doi.org/10.3390/e12112244

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Cadoni M, Melis M.
Entanglement Entropy of AdS Black Holes. *Entropy*. 2010; 12(11):2244-2267.
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**Chicago/Turabian Style**

Cadoni, Mariano, and Maurizio Melis.
2010. "Entanglement Entropy of AdS Black Holes" *Entropy* 12, no. 11: 2244-2267.
https://doi.org/10.3390/e12112244