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We explore the way different loop quantization prescriptions affect theformation of trapped surfaces in the gravitational collapse of a homogeneousdust cloud, with a particular emphasis on the so called $\mu_o$ scheme in whichloop quantum cosmology was initially formulated. Its undesirable features incosmological models led to the so-called improved dynamics or the $\bar \mu$scheme. While the jury is still out on the right scheme for black holespacetimes, we show that as far as the black hole formation is concerned the$\mu_o$ scheme has another, so far unknown, serious problem. We find that inthe $\mu_o$ scheme no trapped surfaces would form for a non-singular collapseof a homogeneous dust cloud in the marginally bound case unless the minimumnon-zero area of the loops over which holonomies are computed or theBarbero-Immirzi parameter decreases almost four times from its standard value.It turns out that the trapped surfaces in the $\mu_o$ scheme for the marginallybound case are also forbidden for any arbitrary matter content as long as thecollapsing interior is isometric to a spatially flatFriedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime. We find that incontrast to the situation in the $\mu_o$ scheme, black holes can form in the$\bar \mu$ scheme, and also other lattice refinements with a mass gapdetermined by quantum geometry.

Does loop quantum $\mu_o$ scheme permit a black hole formation?