Gravitational Collapse via Wheeler-DeWitt Equation
arXiv:2401.07512 · doi:10.1016/j.aop.2023.169579
Abstract
We analyze the Wheeler-DeWitt (WDW) equation in the context of a gravitational collapse. The physics of an expanding/collapsing universe and many details of a collapsing star can classically be described by the Roberston-Walker metric in which the WDW equation takes the form of a times-less Schrödinger equation. We set up the corresponding WDW potential for the collapse and study the solutions of the wave function. The results show that the central singularity appearing in classical general relativity is avoided, the density is quantized in terms of the Planck density and the expectation value of the scale factor exhibits a discrete behavior.
arXiv comment14 pages, 2 figures
References in corpus (27)
- Noncommutative Black Holes, The Final Appeal To Quantum Gravity: A Review
- Action functionals for relativistic perfect fluids
- A Classical Sequential Growth Dynamics for Causal Sets
- Nonminimal coupling of perfect fluids to curvature
- A Short Review of Loop Quantum Gravity
- Approaches to Quantum Cosmology
- Discrete approaches to quantum gravity in four dimensions
- Relativity without relativity
- Loop Quantum Gravity: An Inside View
- Classical collapse to black holes and quantum bounces: A review
- Operator ordering and consistency of the wavefunction of the Universe
- Factor ordering in standard quantum cosmology
- The No-Boundary Proposal as a Path Integral with Robin Boundary Conditions
- Spontaneous creation of the universe from nothing
- Quantum time scales in alpha tunneling
- The matter Lagrangian of an ideal fluid
- A toy model for a baby universe inside a black hole
- Dynamical interpretation of the wavefunction of the universe
- No Time for Time from No-Time
- Jacobi's Principle and the Disappearance of Time
- Reassessing the problem of time of quantum gravity
- Class of solutions of the Wheeler-DeWitt equation with ordering parameter
- Class of solutions of the Wheeler-DeWitt equation in the Friedmann-Robertson-Walker universe
- Solutions to the Wheeler DeWitt Constraint of Canonical Gravity Coupled to Scalar Matter Fields
- Inflation of small true vacuum bubble by quantization of Einstein-Hilbert action
- A road map for Feynman's adventures in the land of gravitation
- The Classical Equations of Motion of Quantized Gauge Theories, Part I: General Relativity