Linearisation instability of gravity waves?
Abstract
Gravity waves in irrotational dust spacetimes are characterised by nonzero magnetic Weyl tensor . In the linearised theory, the divergence of is set to zero. Recently Lesame et al. [Phys. Rev. D {\bf 53}, 738 (1996)] presented an argument to show that, in the exact nonlinear theory, forces , thus implying a linearisation instability for gravity waves interacting with matter. However a sign error in the equations invalidates their conclusion. Bianchi type V spacetimes are shown to include examples with . An improved covariant formalism is used to show that in a generic irrotational dust spacetime, the covariant constraint equations are preserved under evolution. It is shown elsewhere that does not generate further conditions.
Cite
@article{arxiv.astro-ph/9609198,
title = {Linearisation instability of gravity waves?},
author = {Roy Maartens},
journal= {arXiv preprint arXiv:astro-ph/9609198},
year = {2009}
}
Comments
8 pages Revtex; to appear Phys. Rev. D