Integrability of irrotational silent cosmological models
Abstract
We revisit the issue of integrability conditions for the irrotational silent cosmological models. We formulate the problem both in 1+3 covariant and 1+3 orthonormal frame notation, and show there exists a series of constraint equations that need to be satisfied. These conditions hold identically for FLRW-linearised silent models, but not in the general exact non-linear case. Thus there is a linearisation instability, and it is highly unlikely that there is a large class of silent models. We conjecture that there are no spatially inhomogeneous solutions with Weyl curvature of Petrov type I, and indicate further issues that await clarification.
Keywords
Cite
@article{arxiv.gr-qc/9611002,
title = {Integrability of irrotational silent cosmological models},
author = {H van Elst and C Uggla and W Lesame and G Ellis and R Maartens},
journal= {arXiv preprint arXiv:gr-qc/9611002},
year = {2009}
}
Comments
Minor corrections and improvements; 1 new reference; to appear Class. Quantum Grav.; 16 pages Ioplppt