### Abstract

We perform a canonical analysis of a model in which gravity is coupled to a spherically symmetric dust shell in 2+1 space-time dimensions. The result is a reduced action depending on a finite number of degrees of freedom. We emphasize finding canonical variables supporting a global parameterization for the entire phase space of the model. It turns out that different regions of the momentum space corresponding to different branches of the solution of the Einstein equation form a single manifold in the ADS_{2} geometry. The Euler angles support a global parameterization of that manifold. Quantization in these variables leads to noncommutativity and also to discreteness in the coordinate space, which allows resolving the central singularity. We also find the map between the ADS_{2} momentum space obtained here and the momentum space in Kuchar variables, which could be helpful in extending the obtained results to 3+1 dimensions.

Original language | English |
---|---|

Pages (from-to) | 1269-1281 |

Journal | Theoretical and Mathematical Physics |

Volume | 200 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Sep 2019 |

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### Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Theoretical and Mathematical Physics*,

*200*(3), 1269-1281. https://doi.org/10.1134/S0040577919090022

}

*Theoretical and Mathematical Physics*, vol. 200, no. 3, pp. 1269-1281. https://doi.org/10.1134/S0040577919090022

**(2+1)-Dimensional Gravity Coupled to a Dust Shell : Quantization in Terms of Global Phase Space Variables.** / Andrianov, A. A.; Starodubtsev, A. N.; Elmahalawy, Y.

Research output

TY - JOUR

T1 - (2+1)-Dimensional Gravity Coupled to a Dust Shell

T2 - Quantization in Terms of Global Phase Space Variables

AU - Andrianov, A. A.

AU - Starodubtsev, A. N.

AU - Elmahalawy, Y.

N1 - Andrianov, A.A., Starodubtsev, A.N. & Elmahalawy, Y. Theor Math Phys (2019) 200: 1269. https://doi.org/10.1134/S0040577919090022

PY - 2019/9/1

Y1 - 2019/9/1

N2 - We perform a canonical analysis of a model in which gravity is coupled to a spherically symmetric dust shell in 2+1 space-time dimensions. The result is a reduced action depending on a finite number of degrees of freedom. We emphasize finding canonical variables supporting a global parameterization for the entire phase space of the model. It turns out that different regions of the momentum space corresponding to different branches of the solution of the Einstein equation form a single manifold in the ADS2 geometry. The Euler angles support a global parameterization of that manifold. Quantization in these variables leads to noncommutativity and also to discreteness in the coordinate space, which allows resolving the central singularity. We also find the map between the ADS2 momentum space obtained here and the momentum space in Kuchar variables, which could be helpful in extending the obtained results to 3+1 dimensions.

AB - We perform a canonical analysis of a model in which gravity is coupled to a spherically symmetric dust shell in 2+1 space-time dimensions. The result is a reduced action depending on a finite number of degrees of freedom. We emphasize finding canonical variables supporting a global parameterization for the entire phase space of the model. It turns out that different regions of the momentum space corresponding to different branches of the solution of the Einstein equation form a single manifold in the ADS2 geometry. The Euler angles support a global parameterization of that manifold. Quantization in these variables leads to noncommutativity and also to discreteness in the coordinate space, which allows resolving the central singularity. We also find the map between the ADS2 momentum space obtained here and the momentum space in Kuchar variables, which could be helpful in extending the obtained results to 3+1 dimensions.

KW - quantum gravity

KW - singularity removal

KW - thin shell

UR - http://www.scopus.com/inward/record.url?scp=85073265743&partnerID=8YFLogxK

U2 - 10.1134/S0040577919090022

DO - 10.1134/S0040577919090022

M3 - Article

AN - SCOPUS:85073265743

VL - 200

SP - 1269

EP - 1281

JO - Theoretical and Mathematical Physics

JF - Theoretical and Mathematical Physics

SN - 0040-5779

IS - 3

ER -