A singularity theorem based on spatial averages
Abstract
Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating everywhere expanding universes with non-vanishing spatial average of the matter variables are severely geodesically incomplete to the past. Another way of stating the result is that, under the same conditions, any singularity-free model must have a vanishing spatial average of the energy density (and other physical variables). This is very satisfactory and provides a clear decisive difference between singular and non-singular cosmologies.
Cite
@article{arxiv.gr-qc/0610127,
title = {A singularity theorem based on spatial averages},
author = {José M. M. Senovilla},
journal= {arXiv preprint arXiv:gr-qc/0610127},
year = {2008}
}
Comments
Corrections made in the main theorem and related places. 16 pages, no figures. Invited contribution to the Pramana special issue, dedicated to A K Raychaudhuri, on "the Raychaudhuri Equation and its Role in Modern Cosmology" (Edited by Naresh Dadhich, Pankaj Joshi and Probir Roy). Final version to be published