Effective Quantum Dust Collapse via Surface Matching

Abstract

The fate of matter forming a black hole is still an open problem, although models of quantum gravity corrected black holes are available. In loop quantum gravity (LQG) models were presented, which resolve the classical singularity in the centre of the black hole by means of a black-to-white hole transition, but neglect the collapse process. The situation is similar in other quantum gravity approaches, where eternal non-singular models are available. In this paper, a strategy is presented to generalise these eternal models to dynamical collapse models by surface matching. Assuming 1) the validity of a static quantum black hole spacetime outside the collapsing matter, 2) homogeneity of the collapsing matter, and 3) differentiability at the surface of the matter fixes the dynamics of the spacetime uniquely. It is argued that these assumptions resemble a collapse of pressure-less dust and thus generalises the Oppenheimer-Snyder-Datt model, although no precise model of the matter has to be assumed. Hawking radiation is systematically neglected in this approach. The junction conditions and the spacetime dynamics are discussed generically for bouncing black hole spacetimes, as proposed by LQG, although the scheme is approach independent. Further, the equations are explicitly solved for the recent model [1] and a global spacetime picture of the collapse is achieved. The causal structure is discussed in detail and the Penrose diagram is constructed. The trajectory of the collapsing matter is completely constructed from an inside and outside observer point of view. The general analysis shows that the matter is collapsing and re-expanding and crosses the Penrose diagram diagonally. This way the infinite tower of Penrose diagrams, as proposed by several LQG models, is generically not cut out. Questions about different timescales of the collapse for in- and outside observers can be answered.

arXiv comment40 pages, 23 figures. Version accepted for publication in CQG. Minor changes, clarifications added

References in corpus (67)

• Formation and evaporation of non-singular black holes
• Quantum Nature of the Big Bang: Improved dynamics
• Noncommutative Black Holes, The Final Appeal To Quantum Gravity: A Review
• Notes on non-singular models of black holes
• Black hole evaporation: A paradigm
• Quantum Transfiguration of Kruskal Black Holes
• Black hole fireworks: quantum-gravity effects outside the horizon spark black to white hole tunneling
• Quantum Extension of the Kruskal Space-time
• Loop Quantum Dynamics of the Schwarzschild Interior
• Space-Time Structure of Loop Quantum Black Hole
• White Holes as Remnants: A Surprising Scenario for the End of a Black Hole
• Loop quantization of the Schwarzschild interior revisited
• Non-singular quantum-inspired gravitational collapse
• Classical collapse to black holes and quantum bounces: A review
• "Kerrr" black hole: the Lord of the String
• A black hole mass threshold from non-singular quantum gravitational collapse
• A model for non-singular black hole collapse and evaporation
• Effective loop quantum gravity framework for vacuum spherically symmetric space-times
• Effective line elements and black-hole models in canonical (loop) quantum gravity
• Cosmological Effective Hamiltonian from full Loop Quantum Gravity Dynamics
• Conservative solutions to the black hole information problem
• Effective Quantum Extended Spacetime of Polymer Schwarzschild Black Hole
• Quantum Corrected Black Holes from String T-Duality
• Dynamical renormalization of black-hole spacetimes
• Covariance in models of loop quantum gravity: Spherical symmetry
• Self-dual Black Holes in LQG: Theory and Phenomenology
• A consistent model of non-singular Schwarzschild black hole in loop quantum gravity and its quasinormal modes
• The lifetime problem of evaporating black holes: mutiny or resignation
• Spherically symmetric loop quantum gravity: analysis of improved dynamics
• Regular black holes with stable cores
• Polymer Schwarzschild black hole: An effective metric
• Critical evaluation of common claims in loop quantum cosmology
• Black hole collapse and bounce in effective loop quantum gravity
• Singularities and Quantum Gravity
• (b,v)-type variables for black to white hole transitions in effective loop quantum gravity
• The classical double copy of non-singular black holes
• Simple Analytic Models of Gravitational Collapse
• Singularity avoidance for collapsing quantum dust in the Lemaitre-Tolman-Bondi model
• Mass and Horizon Dirac Observables in Effective Models of Quantum Black-to-White Hole Transition
• Properties of a recent quantum extension of the Kruskal geometry
• Towards conditions for black-hole singularity-resolution in asymptotically safe quantum gravity
• Perspectives on the dynamics in a loop quantum gravity effective description of black hole interiors
• A no-go result for covariance in models of loop quantum gravity
• Black hole singularity resolution via the modified Raychaudhuri equation in loop quantum gravity
• Bouncing compact objects I: Quantum extension of the Oppenheimer-Snyder collapse
• Asymptotic non-flatness of an effective black hole model based on loop quantum gravity
• Evaporating black-to-white hole
• Towards a quantum Oppenheimer-Snyder model
• Bouncing compact objects. Part II: Effective theory of a pulsating Planck star
• Quantum Oppenheimer-Snyder model
• Remarks on non-singular black holes
• Gravitational collapse in loop quantum gravity
• Symmetries of the Black Hole Interior and Singularity Regularization
• Quantum dynamics of the black hole interior in LQC
• Black hole evaporation and semiclassical thin shell collapse
• Jebsen-Birkhoff theorem and its stability in f(R) gravity
• A toy model for a baby universe inside a black hole
• Gravitational Collapse for the K-essence Emergent Vaidya Spacetime
• The singularity problem in string theory
• Marginally Trapped Surfaces in Spherical Gravitational Collapse
• Classical polymerization of the Schwarzschild metric
• On the quantum improved Schwarzschild black hole
• Hamiltonian formalism for the Oppenheimer-Snyder model
• On Birkhoff's Theorem in Horava Gravity
• Remarks on regular black holes
• Critical behaviour in quantum gravitational collapse
• Generalized Birkhoff theorem and its applications in mimetic gravity

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• Improved Effective Dynamics of Loop-Quantum-Gravity Black Hole and Nariai Limit
• The End of a Black Hole's Evaporation -- Part II
• Causal Structure of a recent Loop Quantum Gravity Black Hole Collapse Model
• Gravitational collapse in effective loop quantum gravity: beyond marginally bound configurations
• Quantum Corrected Polymer Black Hole Thermodynamics: Mass Relations and Logarithmic Entropy Correction
• Decoding quantum gravity information with black hole accretion disk
• Group quantization of the black hole minisuperspace
• Effective Quantum Gravitational Collapse in a Polymer Framework
• A spin foam framework for the black-to-white hole transition
• Hidden Symmetries in Gravity : Black holes and other minisuperspaces