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

TL;DR

This work develops a Hamiltonian Israel-junction framework for a dust thin shell in an effective loop-quantum-gravity inspired spacetime, ensuring the shell remains timelike throughout its evolution. The key result is a closed effective equation of motion for the shell, which exhibits a quantum bounce at a Planckian density and then re-expands, effectively modeling post-bounce stellar dynamics beyond shell-crossing. The exterior vacuum resembles the OS scenario but with quantum-corrected interiors and a deformed covariance, leading to a physically meaningful continuation of spacetime beyond shell-crossing singularities. While insightful, the approach remains a toy model with open questions about white-hole stability, information loss, and how additional quantum-gravity effects might alter the exterior or suppress SCS; future work could address these issues and include pressure or dispersion effects to refine the collapse picture.

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.