1+1+2 gravitational perturbations on LRS class II space-times: GEM vector harmonic amplitudes
General Relativity and Quantum Cosmology
2007-08-21 v1
Abstract
This is the second in a series of papers which considers first-order gauge-invariant and covariant gravitational perturbations to locally rotationally symmetric (LRS) class II space-times. This paper shows how to decouple a complex combination of the gravito-electromagnetic (GEM) 2-vectors with the 2-tensors describing the shear of the 2/3-sheets. An arbitrary harmonic expansion is then used along with an eigen-vector/value analysis of the first-order GEM system, analogous to the first paper in this series. This results in four real decoupled equations governing four real combinations of the harmonic amplitudes of the GEM 2-vectors and the (2/3-sheet) shear 2-tensors. Finally, these are categorized into polar and axial perturbations.
Cite
@article{arxiv.0708.2558,
title = {1+1+2 gravitational perturbations on LRS class II space-times: GEM vector harmonic amplitudes},
author = {R. B. Burston},
journal= {arXiv preprint arXiv:0708.2558},
year = {2007}
}