A loop quantization of the marginally bound Lemaître-Tolman-Bondi dust model

Abstract

We present a loop quantization of the marginally bound Lemaître-Tolman-Bondi (LTB) model, describing the gravitational collapse of pressureless dust in spherical symmetry. The full quantum LTB model is constructed as a collection of non-interacting shells, each governed by an individual single-shell loop quantum dynamics. We show that the single-shell evolution is non-singular and that wave packets initially peaked on a collapsing trajectory undergo a bounce at Planckian energy densities and subsequently follow an expanding classical trajectory, resolving the classical central curvature singularity. We also compare the loop quantum theory with the Wheeler-DeWitt quantization of the same model. Finally, we briefly comment on the accuracy of the loop quantum gravity effective theory in reproducing this full quantum dynamics. Specifically, we find that initially collapsing wave packets generically develop an interference pattern at the bounce, which suppresses the accuracy of the effective theory near the center of the dust cloud.

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