Does the Loop Quantum μo Scheme Permit Black Hole Formation? - Bao-Fei Li (MDPI AG, 2021)
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 <semantics>μo</semantics> scheme in which loop quantum cosmology was initially formulated. Its undesirable features in cosmological models led to the so-called improved dynamics or the <semantics><mover accent="true">μ¯</mover></semantics> 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 <semantics>μo</semantics> scheme has another, so far unknown, serious problem. We found that in the <semantics>μo</semantics> 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 <semantics>μo</semantics> 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–Lemaître–Robertson–Walker (FLRW) spacetime. We found that in contrast to the situation in the <semantics>μo</semantics> scheme, black holes can form in the <semantics><mover accent="true">μ¯</mover></semantics> scheme, as well as other lattice refinements with a mass gap determined by quantum geometry.