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

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.

💡 Research Summary

The paper presents a systematic study of dust collapse and possible bounce in a broad class of spherically symmetric, quantum‑inspired gravity models. Starting from a generic static spherically symmetric line element written with three shape functions (h_1(x), h_2(x), h_3(x)), the authors construct a deformed Hamiltonian constraint that reproduces these metrics under dynamical flow. Minimal coupling of a pressure‑less dust field is introduced, and the Hamiltonian is split into gravitational and dust parts with lapse and shift acting as Lagrange multipliers.

Two gauge fixings are applied: the dust‑time gauge (T=t) (so the dust field serves as a physical clock) and the areal gauge (E_x = x^2). These eliminate all constraints, leaving a physical Hamiltonian equal to the gravitational part. The remaining dynamical variables are the angular triad component (E_\phi) and its conjugate curvature (K_\phi). After setting (h_1=1) the equations simplify to a first‑order PDE for (K_\phi) and an expression for the physical Hamiltonian as a spatial derivative of (h_2 h_3 K_\phi^2).

Solving these equations yields \