Quantum effects in a homogeneous dust cloud collapse (Q1093196)

The authors consider conformal fluctuations (restricted to depend only on the time coordinate) of the metric of the Oppenheimer-Snyder solution to the Einstein equations describing the collapse of a homogeneous dust ball. They tacitly assume that the matter contribution to the action is conformally invariant, which is obviously wrong for dust matter. Subject to this assumption the dynamics of the conformal metric scale factor is that of a parametrically excited harmonic oscillator whose frequency diverges as the singularity is approached. As a consequence it is found upon quantization that the mean square deviation of the scale factor diverges, too, in this limit.