Quantum Oppenheimer-Snyder model

We construct two reduced quantum theories for the Oppenheimer-Snyder model, respectively taking the point of view of the comoving and the exterior stationary observer, using affine coherent states quantization. Investigations of the quantum corrected dynamics reveal that both observers can see a bounce, although for the exterior observer certain quantization ambiguities have to be chosen correctly. The minimal radius for this bounce as seen from the stationary observer is then shown to always be outside of the photon sphere. Possible avenues to lower this minimal radius and reclaim black holes as an intermediate state in the collapse are discussed. We demonstrate further that switching between the observers at the level of the quantum theories can be achieved by modifying the commutation relations.

Figure 1

The quantum corrected phase space portraits for the outside branch of the Hamiltonian as given by (10) (full green line) as compared to their classical counterpart (dotted red line), given by $M=\sqrt{\frac{A}{2}}{\tanh }^2{P}_A$, and the horizon $M=\sqrt{\frac{A}{2}}$ (dashed blue line), in Planck units.

Figure 2

The quantum corrected phase space portraits for the inside branch of the Hamiltonian as given by (10) (full green line) as compared to their classical counterpart (dotted red line), given by $M=\sqrt{\frac{A}{2}}{\coth }^2{P}_A$, and the horizon $M=\sqrt{\frac{A}{2}}$ (dashed blue line), in Planck units.

Figure 3

The quantum corrected trajectories for the outside branch (full green lines) and inside branch (dotted dashed yellow lines) of the Hamiltonian (9) for different initial conditions as compared to their classical counterparts (dotted red lines) and the horizon $M=\sqrt{\frac{A}{2}}$ (dashed blue lines), in Planck units.

Figure 4

The quantum corrected phase space portraits at $P_A=0$ for the outside and inside branch of the Hamiltonian as given by (10) for different $\beta$ (green lines) as compared to the horizon $M=\sqrt{\frac{A}{2}}$ (dashed blue line) and the photon sphere $M=\frac{\sqrt{2A}}{3}$ (full red line), in Planck units.