On the behaviour of non-radial null geodesics in self-similar Tolman-Bondi collapse
arXiv:1503.08344 · doi:10.1088/1742-6596/1208/1/012010
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.
12 pages, 4 figures. Prepared for the proceedings of the workshop to pay homage to Victor Manuel Villanueva Sandoval. Morelia, México, December 2013