Non-singular quantum gravitational dynamics of an LTB dust shell model:
  the role of quantization prescriptions
  We study some consequences of the loop quantization of the outermost dust
shell in the Lema\^itre-Tolman-Bondi spacetime with a homogeneous dust density
using different quantization strategies motivated by loop quantum gravity.
Prior work has dealt with loop quantizing this model by employing holonomies
and the triads, following the procedure in standard loop quantum cosmology. In
this work we compare this quantization with the one in which holonomies and
gauge-covariant fluxes are used. While both of the quantization schemes resolve
the central singularity, they lead to different mass gaps at which a trapped
surface forms. This trapped surface which is matched to an exterior generalized
Vaidya spacetime disappears when the density of the dust shell is in the Planck
regime. We find that the quantization based on holonomies and gauge-covariant
fluxes generically results in an asymmetric evolution of the dust shell in
which the effective mass associated with the white hole as seen by an external
observer is $2/\pi$ of the one for the black hole. This effective difference in
masses results from difference in the classical limits in pre- and post-bounce
regimes in the two quantizations. This distinctive feature rules out formation
of any black hole-white hole twin in presence of gauge-covariant flux
modifications which is in contrast to the quantization using holonomies and
triads where the gravitational collapse always leads to a black hole-white hole
twins. In another striking difference, for the quantization based on holonomies
and gauge-covariant fluxes there can be situations in which during a
non-singular collapse only a black hole forms without a white hole.
