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

We develop an algebraic equation to describe the collapse and possible bounce of dust in quantum-inspired gravity models with spherical symmetry from knowledge of the vacuum solution. 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. 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 metric shape functions are obtained. The dust density is not assumed to be homogeneous inside the collapsing ball. Using the developed algebraic equations, we examine several quantum-inspired gravity metrics to obtain bounce results either previously obtained by different methods or new results.