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

TL;DR

This paper investigates how different loop quantum cosmology schemes influence black hole formation, revealing that the traditional $rac{}{}$ scheme prevents trapped surface formation unless parameters are significantly altered, unlike the improved $ar rac{}{}$ scheme which allows black hole formation.

Contribution

It demonstrates that the $rac{}{}$ scheme has fundamental issues preventing black hole formation, highlighting the importance of the $ar rac{}{}$ scheme for realistic models.

Findings

The $rac{}{}$ scheme forbids trapped surfaces unless parameters are altered.

Black holes can form in the $ar rac{}{}$ scheme and other lattice models.

Trapped surface formation depends critically on the quantization scheme used.

Abstract

We explore the way different loop quantization prescriptions affect the formation of trapped surfaces in the gravitational collapse of a homogeneous dust cloud, with a 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 $\bar \mu$ scheme. While the jury is still out on the right scheme for black hole spacetimes, 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 in the $\mu_o$ scheme no trapped surfaces would form for a non-singular collapse of a homogeneous dust cloud in the marginally bound case unless the minimum non-zero 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 any arbitrary matter content as long as the collapsing interior is isometric to a spatially flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime. We find that in contrast 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 gap determined by quantum geometry.