Quantum gravitational stellar evolution beyond shell-crossing singularities

TL;DR

This paper develops a Hamiltonian framework to extend stellar evolution models inspired by loop quantum gravity beyond shell-crossing singularities, resulting in an inter-universal wormhole formation.

Contribution

It introduces a novel method to treat shell-crossing singularities as thin dust shells, enabling continuous evolution and wormhole formation in quantum gravity-inspired stellar collapse models.

Findings

Shell-crossing singularities can be modeled as non-isolated thin shells.

The approach maintains a timelike shell throughout collapse.

Results suggest formation of inter-universal wormholes.

Abstract

Models of effective stellar collapse inspired by loop quantum gravity predict a bounce when the stellar energy density reaches the Planck scale, typically followed by the formation of shell-crossing singularities. This work aims to extend the spacetime beyond these singularities by employing a Hamiltonian formulation of the Darmois-Israel junction conditions, treating the singularity as a non-isolated thin dust shell. By construction, the shell's motion remains timelike throughout the entire evolution, regardless of the amount of initial stellar mass, and the induced metric on the shell remains continuous. The resulting stellar evolution produces an inter-universal wormhole, analogous to the simpler Oppenheimer-Snyder scenario. The proposed approach provides a general framework for any effective (or classical) theory of stellar collapse characterized by shell-crossing singularities.