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 ADS2-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.

Original languageEnglish
Article number2040031
Number of pages4
JournalInternational Journal of Modern Physics A
Volume35
Issue number2-3
DOIs
StatePublished - 30 Jan 2020

    Scopus subject areas

  • Astronomy and Astrophysics
  • Nuclear and High Energy Physics
  • Atomic and Molecular Physics, and Optics

    Research areas

  • Quantum gravity, singularity avoidance, thin shell, GEOMETRODYNAMICS

ID: 53624282