Locally Rotationally Symmetric Class II Space-time Perturbations by Electromagnetic, Gravitational, and Plasma Effects

We look at first-order perturbations on homogeneous and hypersurface orthogonal LRS class II spacetimes that are gravitational, electromagnetic, and plasma-related. The examined backgrounds' anisotropy allows us to add a nonzero magnetic field up to the zeroth order. Due to this inclusion, we discover intriguing interactions between the electromagnetic and gravitational variables in the perturbations that are already of the first order. The Ricci identities, Bianchi identities, Maxwell's equations, Einstein's field equations, particle conservation, and an energy-momentum conservation method for the plasma components are all used to get the equations regulating these perturbations. The analyzed quantities and equations are decomposed with regard to the preferred directions on a 1 + 1 + 2 covariant split of space-time. The system is then reduced to a set of ordinary differential equations in time and certain constraints by linearizing the decomposed equations around an LRS background, carrying out a harmonic decomposition, and imposing the cold Magneto Hydrodynamic (MHD) limit with a limited electrical resistivity. The system decouples into two closed and independent subsectors once some harmonic coefficients are solved for in terms of the others. We then examine various methods for producing magnetic field perturbations by numerical calculations, which exhibit certain characteristics like those of earlier research utilising Friedmann-LemaîtreRobertson-Walker (FLRW) backgrounds. Furthermore, due to interference between gravitational waves and plasmonic modes in the short wavelength limit, beat-like patterns are seen.