# Brief Review on Black Hole Loop Quantization

## Abstract

**:**

## 1. Introduction

## 2. Classical System

#### 2.1. Kinematics

#### 2.2. Weak Dirac Observables

#### 2.3. Abelianization of the Hamiltonian Constraint

## 3. Kinematical Hilbert Space

## 4. Representation of the Hamiltonian Constraint

## 5. Solutions to the Hamiltonian Constraint

#### 5.1. Solutions for ${F}_{j}<0$

#### 5.2. Solutions for ${F}_{j}>0$

## 6. Physical Hilbert Space and Observables

## 7. Comparison with Previous Quantizations

#### 7.1. Interior of the Black Hole: Kantowski–Suchs Spacetimes

#### 7.2. Exterior of the Black Hole: Schwarzschild Spacetime

## 8. The Reissner–Nordström Black Hole

## 9. Quantum Test Fields on Quantum Geometries

#### 9.1. Casimir Effect

#### 9.2. Hawking Radiation

## 10. Coupling to a Spherically-Null Dust Shell

## 11. Conclusions

## Acknowledgments

## Conflicts of Interest

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Olmedo, J.
Brief Review on Black Hole Loop Quantization. *Universe* **2016**, *2*, 12.
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Olmedo J.
Brief Review on Black Hole Loop Quantization. *Universe*. 2016; 2(2):12.
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**Chicago/Turabian Style**

Olmedo, Javier.
2016. "Brief Review on Black Hole Loop Quantization" *Universe* 2, no. 2: 12.
https://doi.org/10.3390/universe2020012