### 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 |
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Pages (from-to) | 1269-1281 |

Journal | Theoretical and Mathematical Physics |

Volume | 200 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Sep 2019 |

### Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics