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Description
We present a loop quantization of the marginally bound Lemaitre-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 noninteracting 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. Specifically, we find that expectation values associated with sharply peaked wave packets closely follow their semiclassical counterparts throughout the evolution, except near the bounce, where quantum interference effects typically arise, limiting the validity of the effective theory.
Unlike the semiclassical theory, access to a fully quantum description may open the possibility of formulating quantum field theory on quantum spacetimes, with potential applications to Hawking radiation and black holes thermodynamics.