1+1+2 gravitational perturbations on LRS class II space-times: GEM scalar harmonic amplitudes

TL;DR

This paper completes the analysis of gauge-invariant gravitational perturbations in LRS class II space-times by deriving three decoupled equations for gravito-electromagnetic scalar fields, advancing understanding of their perturbative structure.

Contribution

It introduces a method to derive three decoupled equations for GEM scalar fields in LRS class II space-times, completing previous analyses.

Findings

Derived three decoupled equations for GEM scalar fields.

Identified equations for gravito-magnetic and gravito-electric scalar derivatives.

Enhanced the theoretical framework for gravitational perturbations in LRS space-times.

Abstract

This is the third in a series of papers which considers first-order gauge-invariant and covariant gravitational perturbations to locally rotationally symmetric (LRS) class II space-times. In this paper we complete our analysis of the first-order gravito-electromagnetic (GEM) system by showing how to derive three decoupled equations governing the GEM scalar fields. One of these is for the gravito-magnetic scalar, whereas another two arise from the 2-gradient of the gravito-electric scalar.