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

We investigate electromagnetic, gravitational, and plasma related perturbations to first order on homogeneous and hypersurface orthogonal locally rotationally symmetric (LRS) class II spacetimes. Due to the anisotropic nature of the studied backgrounds, we are able to include a non-zero magnetic field to zeroth order. As a result of this inclusion, we find interesting interactions between the electromagnetic and gravitational variables already to first order in the perturbations. The equations governing these perturbations are found by using the Ricci identities, the Bianchi identities, Einstein's field equations, Maxwell's equations, particle conservation, and a form of energy-momentum conservation for the plasma components. Using a $1+1+2$ covariant split of spacetime, the studied quantities and equations are decomposed with respect to the preferred directions on the background spacetimes. After linearizing the decomposed equations around a LRS background, performing a harmonic decomposition, and imposing the cold magnetohydrodynamic (MHD) limit with a finite electrical resistivity, the system is then reduced to a set of ordinary differential equations in time and some constraints. On solving for some of the harmonic coefficients in terms of the others, the system is found to decouple into two closed and independent subsectors. Through numerical calculations, we then observe some mechanisms for generating magnetic field perturbations, showing some traits similar to previous works using FLRW backgrounds. Furthermore, beat-like patterns are observed in the short wave length limit due to interference between gravitational waves and plasmonic modes.Comment: 30 pages, 4 figure

General Perturbations of Homogeneous and Orthogonal Locally Rotationally Symmetric Class II Cosmologies with Applications to Dissipative Fluids

First order perturbations of homogeneous and hypersurface orthogonal LRS (Locally Rotationally Symmetric) class II cosmologies with a cosmological constant are considered in the framework of the 1+1+2 covariant decomposition of spacetime. The perturbations, which are for a general energy-momentum tensor, include scalar, vector and tensor modes and extend some previous works where matter was assumed to be a perfect fluid. Through a harmonic decomposition, the system of equations is then transformed to evolution equations in time and algebraic constraints. This result is then applied to dissipative one-component fluids, and on using the simplified acausal Eckart theory the system is reduced to two closed subsystems governed by four and eight harmonic coefficients for the odd and even sectors respectively. The system is also seen to close in a simplified causal theory. It is then demonstrated, within the Eckart theory, how vorticity can be generated from viscosity.Comment: 27 pages, 1 figur

Dissipative Perturbations on LRS Class II Cosmologies Using the 1+1+2 Covariant Split of Spacetime

By including dissipative fluxes in the description, this thesis extends previous results regarding first order perturbations on homogeneous and hypersurface orthogonal locally rotationally symmetric (LRS) class II cosmologies using the 1 + 1 + 2 covariant split of spacetime. Whereas previous works consider perturbations of perfect fluid type, perturbations pertaining to heat flux and fluid viscosity are here studied with the aim to ascertain their effect on the evolution of the fluid vorticity. The studied perturbations include scalar, vector, and tensor modes, and are harmonically decomposed to yield a system of ordinary differential equations. These equations, originating from the Bianchi identities, the Ricci identities for certain preferred vector fields, and the thermodynamic Eckart theory, then decouple into two independent systems. These separately closed systems, with four and eight remaining variables respectively, describe the evolution of perturbations pertaining to the Weyl tensor and the fluid shear, vorticity, heat flow, energy density, and number density. From the final system of equations it is seen that the inclusion of heat flux and fluid viscosity has the possibility to yield mechanisms for generating vorticity, even if this vorticity vanishes initially. This is in contrast to the case of barotropic perfect fluids, for which it can be shown that vorticity perturbations cannot be generated. The validity of the results presented here can be questioned, as the Eckart theory, which violates causality, is employed to describe the detailed thermodynamic properties of the fluid. However, on time scales much larger than the relaxation times of the fluid, it should still provide a decent description of the dissipative phenomena, provided that certain couplings between the dissipative fluxes can be neglected

Dissipative Perturbations on LRS Class II Cosmologies Using the 1+1+2 Covariant Split of Spacetime

By including dissipative fluxes in the description, this thesis extends previous results regarding first order perturbations on homogeneous and hypersurface orthogonal locally rotationally symmetric (LRS) class II cosmologies using the 1 + 1 + 2 covariant split of spacetime. Whereas previous works consider perturbations of perfect fluid type, perturbations pertaining to heat flux and fluid viscosity are here studied with the aim to ascertain their effect on the evolution of the fluid vorticity. The studied perturbations include scalar, vector, and tensor modes, and are harmonically decomposed to yield a system of ordinary differential equations. These equations, originating from the Bianchi identities, the Ricci identities for certain preferred vector fields, and the thermodynamic Eckart theory, then decouple into two independent systems. These separately closed systems, with four and eight remaining variables respectively, describe the evolution of perturbations pertaining to the Weyl tensor and the fluid shear, vorticity, heat flow, energy density, and number density. From the final system of equations it is seen that the inclusion of heat flux and fluid viscosity has the possibility to yield mechanisms for generating vorticity, even if this vorticity vanishes initially. This is in contrast to the case of barotropic perfect fluids, for which it can be shown that vorticity perturbations cannot be generated. The validity of the results presented here can be questioned, as the Eckart theory, which violates causality, is employed to describe the detailed thermodynamic properties of the fluid. However, on time scales much larger than the relaxation times of the fluid, it should still provide a decent description of the dissipative phenomena, provided that certain couplings between the dissipative fluxes can be neglected

Dissipative Perturbations on LRS Class II Cosmologies Using the 1+1+2 Covariant Split of Spacetime

By including dissipative fluxes in the description, this thesis extends previous results regarding first order perturbations on homogeneous and hypersurface orthogonal locally rotationally symmetric (LRS) class II cosmologies using the 1 + 1 + 2 covariant split of spacetime. Whereas previous works consider perturbations of perfect fluid type, perturbations pertaining to heat flux and fluid viscosity are here studied with the aim to ascertain their effect on the evolution of the fluid vorticity. The studied perturbations include scalar, vector, and tensor modes, and are harmonically decomposed to yield a system of ordinary differential equations. These equations, originating from the Bianchi identities, the Ricci identities for certain preferred vector fields, and the thermodynamic Eckart theory, then decouple into two independent systems. These separately closed systems, with four and eight remaining variables respectively, describe the evolution of perturbations pertaining to the Weyl tensor and the fluid shear, vorticity, heat flow, energy density, and number density. From the final system of equations it is seen that the inclusion of heat flux and fluid viscosity has the possibility to yield mechanisms for generating vorticity, even if this vorticity vanishes initially. This is in contrast to the case of barotropic perfect fluids, for which it can be shown that vorticity perturbations cannot be generated. The validity of the results presented here can be questioned, as the Eckart theory, which violates causality, is employed to describe the detailed thermodynamic properties of the fluid. However, on time scales much larger than the relaxation times of the fluid, it should still provide a decent description of the dissipative phenomena, provided that certain couplings between the dissipative fluxes can be neglected

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

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

Electromagnetic, Gravitational, and Plasma-Related Perturbations of Locally Rotationally Symmetric Class II Spacetimes

We investigate electromagnetic, gravitational, and plasma-related perturbations to the first order on homogeneous and hypersurface orthogonal locally rotationally symmetric (LRS) class II spacetimes. Due to the anisotropic nature of the studied backgrounds, we are able to include a non-zero magnetic field to the zeroth order. As a result of this inclusion, we find interesting interactions between the electromagnetic and gravitational variables already of the first order in the perturbations. The equations governing these perturbations are found by using the Ricci identities, the Bianchi identities, Einstein’s field equations, Maxwell’s equations, particle conservation, and a form of energy-momentum conservation for the plasma components. Using a (Formula presented.) covariant split of spacetime, the studied quantities and equations are decomposed with respect to the preferred directions on the background spacetimes. After linearizing the decomposed equations around an LRS background, performing a harmonic decomposition, and imposing the cold magnetohydrodynamic (MHD) limit with a finite electrical resistivity, the system is then reduced to a set of ordinary differential equations in time and some constraints. On solving for some of the harmonic coefficients in terms of the others, the system is found to decouple into two closed and independent subsectors. Through numerical calculations, we then observe some mechanisms for generating magnetic field perturbations, showing some traits similar to previous works using Friedmann–Lemaître–Robertson–Walker (FLRW) backgrounds. Furthermore, beat-like patterns are observed in the short wave length limit due to interference between gravitational waves and plasmonic modes

Perturbations of a class of locally rotationally symmetric cosmologies with applications to dissipative fluids

A gauge invariant perturbation theory, based on the 1 + 1 + 2 covariant split of spacetime, is used to study first order perturbations on a class of anisotropic cosmological backgrounds. The perturbations as well as the energy-momentum tensor are kept general, giving a system of equations on which different physical situations may be imposed. Through a harmonic decomposition, the system is then transformed to evolution equations in time and algebraic constraints. This result is then applied to dissipative one-component fluids, and on using the simplified acausal Eckart theory the system is reduced to two closed subsystems, governed by four and eight harmonic coefficients for the odd and even sectors respectively. The system is also seen to close in a simplified causal theory. It is then demonstrated, within the Eckart theory, how vorticity can be generated from viscosity