1+1+2 gravitational perturbations on LRS class II spacetimes: II. Decoupling gravito-electromagnetic 2-vector and scalar harmonic amplitudes

R B Burston
2008 Classical and quantum gravity  
This is the second paper in a series that considers first-order, gauge-invariant and covariant, gravitational perturbations to locally rotationally symmetric (LRS) class II vacuum spacetimes. Focusing on the 1+1+2 gravito-electromagnetic (GEM) formalism, the first paper used linear algebra techniques to derive four decoupled equations that govern four specific combinations of the GEM 2tensor harmonic amplitudes. This paper completes the decoupling of the 1+1+2 GEM system by showing how to
more » ... howing how to derive seven new decoupled quantities. Four of these arise when considering the GEM 2-vector harmonic amplitudes and it is found that decoupling is achieved by combining these with the (2/3-sheet) shear 2-tensor harmonic amplitudes. The remaining three arise from the 1+1+2 GEM scalars. Two of which concern the 2-gradient of the gravito-electric scalar that must also be combined with shear 2-tensor amplitudes, whereas the other involves the gravito-magnetic scalar only.
doi:10.1088/0264-9381/25/23/235004 fatcat:r3ipwbmnt5fz3kp7fhwooh2oke