Effective LQG-inspired dynamics of a thin shell and the fate of a collapsing star

Abstract

Effective models inspired by loop quantum gravity typically resolve the central singularity by replacing it with a bounce of the matter density in the Planckian regime. In the specific model analyzed here, this bounce is generally followed by the formation of shell-crossing singularities. The purpose of this work is to provide a physically meaningful extension of spacetime beyond the shell-crossing singularity. To this end, we derive the dynamics of a dust thin shell within the effective Hamiltonian framework. The motion of the shell remains timelike throughout: after undergoing a quantum-gravitational bounce, it expands and eventually emerges from the white-hole vacuum region.