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

Abstract

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 energymomentum 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.

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

“…V, can be found in appendix C. However, here we encounter a difficulty which was not present in previous papers. At this point in previous works, the system effectively divides into two separate parts, one containing the odd coefficients and another containing the even parts [12][13][14]. One exception to the division into even and odd equations, which is also present in previous works, are quantities defined using a Levi-Civita psuedo-tensor, such as the vorticity and the magnetic part of the Weyl tensor.…”

“…However, not all quantities are zero on the background. Thus, to represent the perturbations of the quantities in S (0) , we will follow [11][12][13][14] and make use of the spatial gradients of these quantities, as these gradients vanish on the background due to the assumed homogeneity. We therefore introduce the following gauge invariant variables…”

“…Here we state the harmonic decompositions of the linearized equations. Since the equations originating from the Ricci and Bianchi identities can be found in [14], we here only show the additional equations pertaining to the decomposition of the total energy-momentum tensor, energy-momentum and particle conservation for the individual plasma components, and Maxwell's equations.…”

“…Our approach to study these interactions will follow the same steps as in [14], but instead of specializing the equations to describe one-component dissipative fluids, we will consider self-gravitating plasmas. Thus, we will make use of the results for general energy-momentum tensors presented in [14], but we will then close the general system by imposing Maxwell's equations, particle conservation, and equations describing energy-momentum conservation for the plasma components.…”

“…Our approach to study these interactions will follow the same steps as in [14], but instead of specializing the equations to describe one-component dissipative fluids, we will consider self-gravitating plasmas. Thus, we will make use of the results for general energy-momentum tensors presented in [14], but we will then close the general system by imposing Maxwell's equations, particle conservation, and equations describing energy-momentum conservation for the plasma components. In doing so, this article reproduces the methods and equations from [17] and an upcoming contribution to the proceedings from the sixteenth Marcel Grossmann meeting on general relativity [18], but extends these accounts with additional numerical results and discussions.…”