Does the Loop Quantum μo Scheme Permit Black Hole Formation?

We explore the way different loop quantization prescriptions affect the formation of trapped surfaces in the gravitational collapse of a homogeneous dust cloud, with particular emphasis on the so-called mu o scheme in which loop quantum cosmology was initially formulated. Its undesirable features in cosmological models led to the so-called improved dynamics or the mu over bar scheme. While the jury is still out on the right scheme for black hole spacetimes, we show that as far as black hole formation is concerned, the mu o scheme has another, so far unknown, serious problem. We found that in the mu o scheme, no trapped surfaces would form for a nonsingular collapse of a homogeneous dust cloud in the marginally bound case unless the minimum nonzero area of the loops over which holonomies are computed or the Barbero-Immirzi parameter decreases almost four times from its standard value. It turns out that the trapped surfaces in the mu o scheme for the marginally bound case are also forbidden for an arbitrary matter content as long as the collapsing interior is isometric to a spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. We found that in contrast to the situation in the mu o scheme, black holes can form in the mu over bar scheme, as well as other lattice refinements with a mass gap determined by quantum geometry.

Automated summary

We investigate how different loop quantization prescriptions affect the formation of trapped surfaces in gravitational collapse, focusing on the mu o scheme and its drawbacks, as well as the improved dynamics in the mu over bar scheme. It is found that trapped surfaces do not form in the mu o scheme for a nonsingular collapse of homogeneous dust cloud unless certain conditions are met, while black holes can form in the mu over bar scheme and other lattice refinements determined by quantum geometry.