3D gravity with dust: Classical and quantum theory

We study the Einstein gravity and dust system in three spacetime dimensions as an example of a nonperturbative 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 Bañados–Teitelboim–Zanelli black hole, static solutions with naked singularities, and traveling 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.