On the behaviour of non-radial null geodesics in self-similar Tolman-Bondi collapse

TL;DR

This paper studies the paths of light rays near singularities in self-similar Tolman-Bondi collapse models, revealing their behavior through an integrable Hamiltonian system analysis.

Contribution

It provides a complete qualitative analysis of null geodesics in self-similar Tolman-Bondi collapse, leveraging the integrability from homothetic symmetry.

Findings

Null geodesics follow predictable phase flows due to integrability.

The structure of singularities influences geodesic behavior.

Self-similarity simplifies the analysis of collapse dynamics.

Abstract

Motivated by recent work on the structure of the singularity in inhomogeneous Tolman-Bondi collapse models, we investigate the behaviour of null geodesics in the particular case where the collapse is self-similar. The presence of the homothetic Killing vector field implies that the geodesic equation can be described by an integrable Hamiltonian system, and exploiting this fact we provide a full qualitative picture for its phase flow.