3D gravity with dust: classical and quantum theory

TL;DR

This paper explores a non-perturbative quantum gravity model in three dimensions with dust, deriving the Hamiltonian theory, finding exact solutions including black holes, and quantizing the wave sector with a focus on metric operators.

Contribution

It provides a complete quantization of the wave sector in 3D gravity with dust, including the definition of a self-adjoint metric operator and analysis of horizon fluctuations.

Findings

Exact solutions include BTZ black holes and naked singularities

Quantization of deficit angles and horizon fluctuations demonstrated

Hamiltonian theory derived in dust time gauge

Abstract

We study the Einstein gravity and dust system in three spacetime dimensions as an example of a non-perturbative quantum gravity model with local degrees of freedom. We derive the Hamiltonian theory in the dust time gauge and show that it has a rich class of exact solutions. These include the Ba\~nados-Teitelboim-Zanelli black hole, static solutions with naked singularities and travelling wave solutions with dynamical horizons. We give a complete quantization of the wave sector of the theory, including a definition of a self-adjoint spacetime metric operator. This operator is used to demonstrate the quantization of deficit angle and the fluctuation of dynamical horizons.