(2+1)-Dimensional Gravity Coupled to a Dust Shell: Quantization in Terms of Global Phase Space Variables

A. A. Andrianov, A. N. Starodubtsev, Y. Elmahalawy

Research output

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 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.

Original languageEnglish
Pages (from-to)1269-1281
JournalTheoretical and Mathematical Physics
Volume200
Issue number3
DOIs
Publication statusPublished - 1 Sep 2019

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Phase Space
Quantization
Shell
Gravity
dust
gravitation
Momentum
Parameterization
Canonical Analysis
Euler Angles
momentum
parameterization
Noncommutativity
Einstein Equations
Branch
Space-time
Degree of freedom
Entire
Singularity
Einstein equations

Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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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 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.",
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author = "Andrianov, {A. A.} and Starodubtsev, {A. N.} and Y. Elmahalawy",
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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

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