On the Interaction Between Electromagnetic, Gravitational, and Plasma Related Perturbations on LRS Class II Spacetimes

Abstract: In this thesis, we investigate the interaction between electromagnetic, gravitational, and plasma related perturbations on homogeneous and hypersurface orthogonal Locally Rotationally Symmetric (LRS) class II spacetimes. By using these spacetimes, which allow for the inclusion of a non-zero magnetic field, as backgrounds in a perturbative approach, we are able to see interactions between the electromagnetic and gravitational variables already to first order in the perturbations. This is in contrast to earlier works using isotropic Friedmann-Lemaı̂tre-Robertson-Walker (FLRW) backgrounds, where one is usually faced with going to second order in the perturbations. To get the equations governing our perturbations, we use a 1+1+2 covariant approach and gather relations from the Ricci and Bianchi identities, Maxwell’s equations, particle conservation, and energy-momentum conservation for the individual plasma components. After linearising these equations around a LRS background, performing a harmonic decomposition, and using the Magnetohydrodynamic (MHD) approximation for a cold plasma, we then arrive at a closed system for the first order perturbations. This system, consisting of ordinary differential equations in time and a set of constraints, is then reduced to two separate subsectors, containing seven and nine variables respectively. These variables include quantities related to the Weyl tensor, the vorticity, and the electromagnetic fields, as well as perturbations in the plasma velocity and energy density. Through numerical calculations, we use the equations for these variables to show that perturbations in the magnetic field can be sourced by perturbations in both the plasma velocity and the gravitational variables. We also observe beat-like interference patterns for large values of the Alfvén velocity. These results can be of interest when considering the large scale cosmic magnetic fields, as their origin still seems to elude us. However, since we neglect thermal pressures and dissipative fluxes, it should be noted that our results are mainly applicable in the limit of low temperature and in cases where the thermal pressure is smaller than the pressure due to the electromagnetic fields.