Algebraic Equations Model Dust Collapse and Bounce

Douglas M. Gingrich has developed an algebraic equation to describe the collapse and possible bounce of dust in quantum-inspired gravity models with spherical symmetry. Published in the journal General Relativity and Gravitation in November 2026, the research provides a new method for analyzing these phenomena using knowledge of the vacuum solution.

The work begins with a wide class of spherically symmetric spacetimes to establish a robust theoretical foundation. Gingrich writes down the covariant Hamiltonian constraints that, under dynamical flow, give rise to metrics associated with many spherically symmetric gravity models. By solving these constraint equations for Hamiltonian evolution, the researcher derives simple equations for the location of the outer boundary of the dust versus time. These equations also determine the apparent horizons in terms of metric shape functions, providing a clear geometric interpretation of the collapse process.

A key feature of this approach is that the dust density is not assumed to be homogeneous inside the collapsing ball.

Using the developed algebraic equations, Gingrich examines several quantum-inspired gravity metrics to obtain specific bounce results. The analysis yields findings that either replicate results previously obtained by different methods or provide new insights into the behavior of dust in these models.

The study is published in Volume 58, article number 126 of General Relativity and Gravitation.

Subject of Research: Algebraic modeling of dust collapse and bounce in quantum-inspired gravity

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

Article References: Gingrich, D. M. (2026). Dust collapse and bounce in spherically symmetric quantum-inspired gravity models. General Relativity and Gravitation, 58(11), Article 126. https://doi.org/10.1007/s10714-026-03632-0

Image Credits: AI Generated

DOI: 10.1007/s10714-026-03632-0

Keywords: quantum gravity, dust collapse, spherical symmetry, Hamiltonian constraints, apparent horizons, General Relativity, spacetime metrics, gravitational bounce, Dust, collapse, bounce, spherically