In effective loop quantum gravity, an infinite family of mathematically equivalent collapse equations produce different weak solutions after shell crossing, so the predicted black hole lifetime (e.g., M^2, M^3, M^4) is not uniquely determined.
Loop quantum cosmology and the k = - 1 RW model
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abstract
The loop quantization of the negatively curved k=-1 RW model poses several technical challenges. We show that the issues can be overcome and a successful quantization is possible that extends the results of the k=0,+1 models in a natural fashion. We discuss the resulting dynamics and show that for a universe consisting of a massless scalar field, a bounce is predicted in the backward evolution in accordance with the results of the k=0,+1 models. We also show that the model predicts a vacuum repulsion in the high curvature regime that would lead to a bounce even for matter with vanishing energy density. We finally comment on the inverse volume modifications of loop quantum cosmology and show that, as in the k=0 model, the modifications depend sensitively on the introduction of a length scale which a priori is independent of the curvature scale or a matter energy scale.
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Non-uniqueness of the shockwave dynamics in effective loop quantum gravity
In effective loop quantum gravity, an infinite family of mathematically equivalent collapse equations produce different weak solutions after shell crossing, so the predicted black hole lifetime (e.g., M^2, M^3, M^4) is not uniquely determined.