Non-singular quantum gravitational dynamics of an LTB dust shell model: the role of quantization prescriptions

Abstract

We study some consequences of the loop quantization of the outermost dust shell in the Lemaître-Tolman-Bondi spacetime with a homogeneous dust density using different quantization strategies motivated by loop quantum gravity. Prior work has dealt with loop quantizing this model by employing holonomies and the triads, following the procedure in standard loop quantum cosmology. In this work we compare this quantization with the one in which holonomies and gauge-covariant fluxes are used. While both of the quantization schemes resolve the central singularity, they lead to different mass gaps at which a trapped surface forms. This trapped surface which is matched to an exterior generalized Vaidya spacetime disappears when the density of the dust shell is in the Planck regime. We find that the quantization based on holonomies and gauge-covariant fluxes generically results in an asymmetric evolution of the dust shell in which the effective mass associated with the white hole as seen by an external observer is $2/\pi$ of the one for the black hole. This effective difference in masses results from difference in the classical limits in pre- and post-bounce regimes in the two quantizations. This distinctive feature rules out formation of any black hole-white hole twin in presence of gauge-covariant flux modifications which is in contrast to the quantization using holonomies and triads where the gravitational collapse always leads to a black hole-white hole twins. In another striking difference, for the quantization based on holonomies and gauge-covariant fluxes there can be situations in which during a non-singular collapse only a black hole forms without a white hole.

20 pages and 5 figures

References in corpus (16)

• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Nature of the Big Bang
• Loop Quantum Dynamics of the Schwarzschild Interior
• Are loop quantum cosmos never singular?
• Black holes in loop quantum gravity: the complete space-time
• From black holes to white holes: a quantum gravitational, symmetric bounce
• Is loop quantization in cosmology unique?
• A black hole mass threshold from non-singular quantum gravitational collapse
• Non-marginal LTB-like models with inverse triad corrections from loop quantum gravity
• Loop quantization of spherically symmetric midi-superspaces : the interior problem
• Numerical evolution of squeezed and non-Gaussian states in loop quantum cosmology
• Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity
• Singularity avoidance for collapsing quantum dust in the Lemaitre-Tolman-Bondi model
• Critical collapse of a scalar field in semiclassical loop quantum gravity
• Resolution of strong singularities and geodesic completeness in loop quantum Bianchi-II spacetimes
• Loop quantization of spherically symmetric midisuperspaces and loop quantum geometry of the maximally extended Schwarzschild spacetime

Cited by in corpus (21)

• Quantum Oppenheimer-Snyder and Swiss Cheese models
• Shadow and stability of quantum-corrected black holes
• Quantum gravity of dust collapse: shock waves from black holes
• On the fate of quantum black holes
• Dust collapse in asymptotic safety: a path to regular black holes
• On the geometry of the black-to-white hole transition within a single asymptotic region
• Black hole image encoding quantum gravity information
• Spherical symmetric gravitational collapse of a dust cloud: polymerized dynamics in reduced phase space
• Gravitational collapse in effective loop quantum gravity: beyond marginally bound configurations
• Shell-crossings and shock formation during gravitational collapse in effective loop quantum gravity
• Revisiting quantum black holes from effective loop quantum gravity
• Understanding quantum black holes from quantum reduced loop gravity
• On consistent gauge fixing conditions in polymerized gravitational systems
• Quantum gravity might restrict a cyclic evolution
• Influence of Quantum Correction on Kerr Black Hole in Effective Loop Quantum Gravity via Shadows and EHT Results
• Circular orbits and accretion disk around a deformed-Schwarzschild black hole in loop quantum gravity
• Formation of nonsingular spherical black holes with holonomy corrections
• Infrared signatures of quantum bounce in a minisuperspace analysis of Lema\^ıtre-Tolman-Bondi dust collapse
• Lessons from gauge fixing and polymerization of loop quantum black holes with a cosmological constant
• Radiative properties of a nonsingular black hole: Hawking radiation and gray-body factor
• A loop quantization of the marginally bound Lemaître-Tolman-Bondi dust model