Cylindrically symmetric 2+1 gravity in terms of global variables:quantum dynamics

TL;DR

This paper quantizes a 2+1 dimensional gravity model coupled with a circular dust shell, revealing non-commutative geometry and a potential resolution of singularities through finite transition amplitudes.

Contribution

It introduces a novel quantization approach for 2+1 gravity with a dust shell, highlighting the global ADS^2 structure and quantum effects like radius discreteness and bounce phenomena.

Findings

Discreteness of shell radius in quantum regime

Finite transition amplitudes indicating singularity resolution

Non-commutative coordinate space in quantum kinematics

Abstract

We perform quantization of a model in which gravity is coupled to a circular dust shell in 2+1 spacetime dimensions. Canonical analysis shows that momentum space of this model is ADS^2-space, and the global chart for it is provided by the Euler angles. In quantum kinematics, this results in non-commutativity in coordinate space and discreteness of the shell radius in timelike region, which includes the collapse point. At the level of quantum dynamics, we find transition amplitudes between zero and non-zero eigenvalues of the shell radius, which describe the rate of gravitational collapse (bounce). Their values are everywhere finite, which could be interpreted as resolution of the central singularity.