# Quantum Analysis of BTZ Black Hole Formation Due to the Collapse of a Dust Shell

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## Abstract

**:**

## 1. Introduction

## 2. 2 + 1 Gravity Coupled to a Dust Shell and Its ADM Canonical Analysis

## 3. Global Parameterization of ADS and BTZ Spacetime

## 4. Action Principle and Symplectic Form

## 5. Constraints

## 6. Derivation of the Constraint Equations

## 7. Quantization

## 8. Quantum Dynamics

## 9. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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1. | The notation for mass here is different from that of the original paper [16] by substituting $-M\to 1-2m$, so that the empty ADS space is recovered at $m=0$. Note also that the cosmological constant is $|\Lambda |=1/{l}^{2}$, where l is the radius of curvature. |

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**MDPI and ACS Style**

Andrianov, A.A.; Starodubtsev, A.; Elmahalawy, Y.
Quantum Analysis of BTZ Black Hole Formation Due to the Collapse of a Dust Shell. *Universe* **2020**, *6*, 201.
https://doi.org/10.3390/universe6110201

**AMA Style**

Andrianov AA, Starodubtsev A, Elmahalawy Y.
Quantum Analysis of BTZ Black Hole Formation Due to the Collapse of a Dust Shell. *Universe*. 2020; 6(11):201.
https://doi.org/10.3390/universe6110201

**Chicago/Turabian Style**

Andrianov, Alexander A., Artem Starodubtsev, and Yasser Elmahalawy.
2020. "Quantum Analysis of BTZ Black Hole Formation Due to the Collapse of a Dust Shell" *Universe* 6, no. 11: 201.
https://doi.org/10.3390/universe6110201