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Dust collapse and bounce in spherically symmetric quantum-inspired gravity models

Douglas M. Gingrich

TL;DR

This work develops a covariant, dust-coupled, quantum-inspired gravity model for spherically symmetric collapse and derives modified LT B dynamics by solving the Hamiltonian constraints under dust-time and areal gauges. It provides a density evolution equation that generally yields inhomogeneous dust distributions and shows how quantum corrections can halt collapse, leading to a bounce at a finite radius and avoiding singularities. The authors analyze several representative metrics—Schwarzschild, loop-quantum-inspired variants, Simpson-Visser, and covariant loop black holes—to illustrate the bounce behavior and horizon structure, including cases with multiple apparent horizons. These results demonstrate that quantum-inspired corrections can convert black-hole formation into a non-singular black-hole to white-hole-like transition, with implications for covariant formulations of quantum gravity and the interpretation of horizons in highly curved spacetimes.

Abstract

We study the collapse and possible bounce of dust in quantum-inspired gravity models with spherical symmetry. Starting from a wide class of spherically symmetric spacetimes, we write down the covariant Hamiltonian constraints that under dynamical flow give rise to metrics of many spherically symmetric gravity models. Gravity is minimally coupled to a dust field. The constraint equations are solved for the Hamiltonian evolution and simple equations for the location of the outer boundary of the dust versus time and the apparent horizons in terms of shape functions are obtained. The dust density is not assumed to be homogeneous inside the collapsing ball. In many cases, the effective quantum gravity effects stop the collapse of the dust matter field, then causes the dust field to expand thus creating a bounce at a minimum radius and avoiding the classical singularity. Using this formalism, we examine several quantum-inspired gravity metrics to obtain bounce results either previously obtained by different methods or new results.

Dust collapse and bounce in spherically symmetric quantum-inspired gravity models

TL;DR

This work develops a covariant, dust-coupled, quantum-inspired gravity model for spherically symmetric collapse and derives modified LT B dynamics by solving the Hamiltonian constraints under dust-time and areal gauges. It provides a density evolution equation that generally yields inhomogeneous dust distributions and shows how quantum corrections can halt collapse, leading to a bounce at a finite radius and avoiding singularities. The authors analyze several representative metrics—Schwarzschild, loop-quantum-inspired variants, Simpson-Visser, and covariant loop black holes—to illustrate the bounce behavior and horizon structure, including cases with multiple apparent horizons. These results demonstrate that quantum-inspired corrections can convert black-hole formation into a non-singular black-hole to white-hole-like transition, with implications for covariant formulations of quantum gravity and the interpretation of horizons in highly curved spacetimes.

Abstract

We study the collapse and possible bounce of dust in quantum-inspired gravity models with spherical symmetry. Starting from a wide class of spherically symmetric spacetimes, we write down the covariant Hamiltonian constraints that under dynamical flow give rise to metrics of many spherically symmetric gravity models. Gravity is minimally coupled to a dust field. The constraint equations are solved for the Hamiltonian evolution and simple equations for the location of the outer boundary of the dust versus time and the apparent horizons in terms of shape functions are obtained. The dust density is not assumed to be homogeneous inside the collapsing ball. In many cases, the effective quantum gravity effects stop the collapse of the dust matter field, then causes the dust field to expand thus creating a bounce at a minimum radius and avoiding the classical singularity. Using this formalism, we examine several quantum-inspired gravity metrics to obtain bounce results either previously obtained by different methods or new results.
Paper Structure (16 sections, 76 equations, 2 figures)

This paper contains 16 sections, 76 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Effective model
  3. Constraint equations and solutions
  4. Dust density
  5. Dust evolution
  6. Apparent horizons
  7. Collapse and bounce
  8. Schwarzschild spacetime
  9. Loop black hole
  10. Simpson-Visser spacetime
  11. Covariant loop black hole
  12. Scale-independent holonomies
  13. Scale-dependent holonomies
  14. Graphical and numerical results
  15. Concluding remarks
  16. ...and 1 more sections

Figures (2)

  • Figure 1: (left) Density and (right) mass of dust versus areal radius inside the outer dust boundary. The parameters have been chosen to give a common minimum radius of $L_0 = 0.2$ (except Schwarzschild) for $M = 1$.
  • Figure 2: (left) Location of the outer boundary of dust $L(t)$ versus time. (right) Location of the outer boundary of dust (solid curves) and apparent horizons (dashed curves) for three representative metrics. The shaded areas are trapped surfaces. The parameters have been chosen to give a common minimum radius of $L_0 = 0.5$ (except Schwarzschild) with $M = 1$.