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

Abstract

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.

30 pages, 4 figures

References in corpus (12)

• On the Origin of Cosmic Magnetic Fields
• A covariant approach for perturbations of rotationally symmetric spacetimes
• Evolution of primordial magnetic fields during large-scale structure formation
• Primordial magnetic helicity evolution with a homogeneous magnetic field from inflation
• Stealth magnetic field in de Sitter spacetime
• On inhomogeneous magnetic seed fields and gravitational waves within the MHD limit
• 1+1+2 Electromagnetic perturbations on general LRS space-times: Regge-Wheeler and Bardeen-Press equations
• Gravitational Waves in Locally Rotationally Symmetric (LRS) Class II Cosmologies
• General Perfect Fluid Perturbations of Homogeneous and Orthogonal Locally Rotationally Symmetric Class II Cosmologies
• General Perturbations of Homogeneous and Orthogonal Locally Rotationally Symmetric Class II Cosmologies with Applications to Dissipative Fluids
• On the Interaction Between Electromagnetic, Gravitational, and Plasma Related Perturbations on LRS Class II Spacetimes
• Cosmic Electromagnetic Fields due to Perturbations in the Gravitational Field

Cited by in corpus (2)

• On the Interaction Between Electromagnetic, Gravitational, and Plasma Related Perturbations on LRS Class II Spacetimes
• General Perturbations of Homogeneous and Orthogonal Locally Rotationally Symmetric Class II Cosmologies with Applications to Dissipative Fluids