Spherical symmetric gravitational collapse of a dust cloud: polymerized dynamics in reduced phase space

Abstract

Based on the effective dynamics in the $\bar{\mu }$ scheme of the spherical symmetry reduced model in the reduced phase space formulation of loop quantum gravity (LQG), we investigate the gravitational collapse of a homogeneous dust cloud, with Gaussian dust serving as both the reference field and the source of the gravitational collapse. The effective dynamics from the considered model for a homogeneous dust cloud reduces precisely to the effective dynamics of loop quantum cosmology (LQC) with extrinsic curvature based K-quantization, indicating that the LQC effective dynamics lives as a subsector of the model presented here. In both the marginally bound and the bound cases of the collapse in effective dynamics, the singularity is resolved and replaced by a bounce. Though quantum geometric modification from spatial curvature is not directly included in the K-quantization it does affect the qualitative dynamics of the collapsing dust cloud in the sense that on the one hand for the marginally bound case, the dust cloud bounces once at fixed maximum energy density and on the other hand for the bound case, the dust cloud undergoes infinite cycles of contraction and expansion at energy densities dependent on the dust mass. Finally, the mass threshold for the formation of a trapped surface in each case is found and the matching conditions between the interior collapsing spacetime and an effective exterior static solution are discussed.

25 pages, 7 figures

References in corpus (29)

• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Nature of the Big Bang
• Loop quantum cosmology of k=1 FRW models
• Loop Quantum Dynamics of the Schwarzschild Interior
• Are loop quantum cosmos never singular?
• From black holes to white holes: a quantum gravitational, symmetric bounce
• Gravity quantized
• Is loop quantization in cosmology unique?
• A geometric perspective on singularity resolution and uniqueness in loop quantum cosmology
• A black hole mass threshold from non-singular quantum gravitational collapse
• Non-marginal LTB-like models with inverse triad corrections from loop quantum gravity
• Quantum gravity of dust collapse: shock waves from black holes
• Path Integrals and the WKB approximation in Loop Quantum Cosmology
• Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity
• Evaporation of 2-Dimensional Black Holes
• On the fate of quantum black holes
• Singularity avoidance for collapsing quantum dust in the Lemaitre-Tolman-Bondi model
• Algebraic Quantum Gravity (AQG) III. Semiclassical Perturbation Theory
• The End of a Black Hole's Evaporation -- Part I
• Properties of the spherically symmetric polymer black holes
• Critical collapse of a scalar field in semiclassical loop quantum gravity
• Loop quantum deparametrized Schwarzschild interior and discrete black hole mass
• Improved Effective Dynamics of Loop-Quantum-Gravity Black Hole and Nariai Limit
• Non-singular quantum gravitational dynamics of an LTB dust shell model: the role of quantization prescriptions
• Loop quantum black hole extensions within the improved dynamics
• Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
• Reduced Phase Space Quantization of Black Holes: Path Integrals, and Effective Dynamics
• Understanding quantum black holes from quantum reduced loop gravity
• On consistent gauge fixing conditions in polymerized gravitational systems

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