Structure formation in the Lemaitre-Tolman model
Abstract
Structure formation within the Lemaitre-Tolman model is investigated in a general manner. We seek models such that the initial density perturbation within a homogeneous background has a smaller mass than the structure into which it will develop, and the perturbation then accretes more mass during evolution. This is a generalisation of the approach taken by Bonnor in 1956. It is proved that any two spherically symmetric density profiles specified on any two constant time slices can be joined by a Lemaitre-Tolman evolution, and exact implicit formulae for the arbitrary functions that determine the resulting L-T model are obtained. Examples of the process are investigated numerically.
Keywords
Cite
@article{arxiv.gr-qc/0106096,
title = {Structure formation in the Lemaitre-Tolman model},
author = {Andrzej Krasinski and Charles Hellaby},
journal= {arXiv preprint arXiv:gr-qc/0106096},
year = {2008}
}
Comments
LaTeX 2e plus 14 .eps & .ps figure files. 33 pages including figures. Minor revisions of text and data make it more precise and consistent. Currently scheduled for Phys Rev D vol 64, December 15 issue