Gravitational versus Magnetohydrodynamic Waves in Curved Spacetime in the Presence of Large-Scale Magnetic Fields

Abstract

The general-relativistic (GR) magnetohydrodynamic (MHD) equations for a conductive plasma fluid are derived and discussed in the curved spacetime described by Thorne’s metric tensor, i.e., a family of cosmological models with inherent anisotropy due to the existence of an ambient, large-scale magnetic field. In this framework, it is examined whether the magnetized plasma fluid that drives the evolution of such a model can be subsequently excited by a transient, plane-polarized gravitational wave (GW) or not. To do so, we consider the associated set of the perturbed equations of motion and integrate them numerically in order to study the evolution of instabilities triggered by the GW propagation. In particular, we examine to what extend perturbations of the electric and/or the magnetic field can be amplified due to a potential energy transfer from the GW to the electromagnetic (EM) degrees of freedom. The evolution of the perturbed quantities depends on four free parameters, namely, the conductivity of the fluid, σ; the speed of sound square, 13<Csc2≡γ<1, which in this model may serve also as a measure of the inherent anisotropy; the GW frequency, ωg; and the associated angle of propagation with respect to the direction of the magnetic field, θ. We find that GW propagation in the anisotropic magnetized medium under consideration does excite several MHD modes; in other words, there is energy transfer from the gravitational to the EM degrees of freedom that can result in the acceleration of charged particles at the spot and in the subsequent damping of the GW.