Gentle spaghettification in effective LQG dust collapse

Abstract

Effective dust collapse inspired by loop quantum gravity predicts two main features for general realistic initial profiles: a quantum gravitational bounce of the stellar core, when the energy density becomes planckian, and shell-crossing singularities, arising within almost a planckian time after the bounce. The aim of this work is to study the mathematical and physical features of the effective spacetime near these singularities, through the Jacobi deviation equation. The results show that the radial and angular deviations between dust particles remain finite at both the bounce and shell-crossing singularity, providing a physical justification for extending the spacetime beyond shell-crossing singularities through weak solutions.