From classical to quantum Oppenheimer-Snyder model: non-marginal case

Abstract

We first present a consistent canonical formulation of the general (non-marginal) Oppenheimer-Snyder model. The switching between comoving and stationary observer is achieved by promoting coordinate transformations between dust proper time and Schwarzschild-Killing time to canonical ones. This leads to a multivalued Hamiltonian which is deparameterizable. We then discuss the quantization of comoving and stationary observers by employing the method of Affine Coherent State Quantization (ACSQ). We thereby demonstrate that under certain conditions the quantum corrected trajectories can replace the classical singularity by a bounce. We then show that both comoving and stationary observers see this bouncing collapse behavior. We finally discuss a switching between these classes of observers at the quantum level.