English

Linearisation instability of gravity waves?

Astrophysics 2009-10-28 v1

Abstract

Gravity waves in irrotational dust spacetimes are characterised by nonzero magnetic Weyl tensor HabH_{ab}. In the linearised theory, the divergence of HabH_{ab} 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, divH=0div H=0 forces Hab=0H_{ab}=0, 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 divH=0Habdiv H=0\neq H_{ab}. 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 \mboxdivH=0\mbox{div} H=0 does not generate further conditions.

Keywords

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