Does the Loop Quantum <i>μ</i><sub>o</sub> Scheme Permit Black Hole Formation?

Does the Loop Quantum <i>μ</i><sub>o</sub> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="...

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Autores principales: Bao-Fei Li, Parampreet Singh
Formato: article
Lenguaje:EN
Publicado: MDPI AG 2021
Materias:
loop quantum cosmology
loop quantum gravity
Elementary particle physics
QC793-793.5
Acceso en línea:https://doaj.org/article/d96c6012b4ee4ba58d78f7f4c6113214
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spelling oai:doaj.org-article:d96c6012b4ee4ba58d78f7f4c61132142021-11-25T19:09:31ZDoes the Loop Quantum <i>μ</i><sub>o</sub> Scheme Permit Black Hole Formation?10.3390/universe71104062218-1997https://doaj.org/article/d96c6012b4ee4ba58d78f7f4c61132142021-10-01T00:00:00Zhttps://www.mdpi.com/2218-1997/7/11/406https://doaj.org/toc/2218-1997We 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>μ</mi><mi>o</mi></msub></semantics></math></inline-formula> scheme in which loop quantum cosmology was initially formulated. Its undesirable features in cosmological models led to the so-called improved dynamics or the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>μ</mi><mo stretchy="false">¯</mo></mover></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>μ</mi><mi>o</mi></msub></semantics></math></inline-formula> scheme has another, so far unknown, serious problem. We found that in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>μ</mi><mi>o</mi></msub></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>μ</mi><mi>o</mi></msub></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>μ</mi><mi>o</mi></msub></semantics></math></inline-formula> scheme, black holes can form in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>μ</mi><mo stretchy="false">¯</mo></mover></semantics></math></inline-formula> scheme, as well as other lattice refinements with a mass gap determined by quantum geometry.Bao-Fei LiParampreet SinghMDPI AGarticleloop quantum cosmologyloop quantum gravityElementary particle physicsQC793-793.5ENUniverse, Vol 7, Iss 406, p 406 (2021)
institution DOAJ
collection DOAJ
language EN
topic loop quantum cosmology
loop quantum gravity
Elementary particle physics
QC793-793.5
spellingShingle loop quantum cosmology
loop quantum gravity
Elementary particle physics
QC793-793.5
Bao-Fei Li
Parampreet Singh
Does the Loop Quantum <i>μ</i><sub>o</sub> Scheme Permit Black Hole Formation?
description 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>μ</mi><mi>o</mi></msub></semantics></math></inline-formula> scheme in which loop quantum cosmology was initially formulated. Its undesirable features in cosmological models led to the so-called improved dynamics or the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>μ</mi><mo stretchy="false">¯</mo></mover></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>μ</mi><mi>o</mi></msub></semantics></math></inline-formula> scheme has another, so far unknown, serious problem. We found that in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>μ</mi><mi>o</mi></msub></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>μ</mi><mi>o</mi></msub></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>μ</mi><mi>o</mi></msub></semantics></math></inline-formula> scheme, black holes can form in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>μ</mi><mo stretchy="false">¯</mo></mover></semantics></math></inline-formula> scheme, as well as other lattice refinements with a mass gap determined by quantum geometry.
format article
author Bao-Fei Li
Parampreet Singh
author_facet Bao-Fei Li
Parampreet Singh
author_sort Bao-Fei Li
title Does the Loop Quantum <i>μ</i><sub>o</sub> Scheme Permit Black Hole Formation?
title_short Does the Loop Quantum <i>μ</i><sub>o</sub> Scheme Permit Black Hole Formation?
title_full Does the Loop Quantum <i>μ</i><sub>o</sub> Scheme Permit Black Hole Formation?
title_fullStr Does the Loop Quantum <i>μ</i><sub>o</sub> Scheme Permit Black Hole Formation?
title_full_unstemmed Does the Loop Quantum <i>μ</i><sub>o</sub> Scheme Permit Black Hole Formation?
title_sort does the loop quantum <i>μ</i><sub>o</sub> scheme permit black hole formation?
publisher MDPI AG
publishDate 2021
url https://doaj.org/article/d96c6012b4ee4ba58d78f7f4c6113214
work_keys_str_mv AT baofeili doestheloopquantumimisubosubschemepermitblackholeformation
AT parampreetsingh doestheloopquantumimisubosubschemepermitblackholeformation
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