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The general-relativistic (GR) magnetohydrodynamic (MHD) equations for aconductive plasma fluid are derived and discussed in the curved spacetimedescribed by Thorne's metric tensor, i.e., a family of cosmological models withinherent anisotropy due to the existence of an ambient, large-scale magneticfield. In this framework, it is examined whether the magnetized plasma fluidthat drives the evolution of such a model can be subsequently excited by atransient, plane-polarized gravitational wave (GW) or not. To do so, weconsider the associated set of the perturbed equations of motion and integrateit numerically, to study the evolution of instabilities triggered by the GWpropagation. In particular, we examine to what extend perturbations of theelectric- and/or the magnetic field can be amplified due to a potential energytransfer from the GW to the electromagnetic (EM) degrees of freedom. Theevolution of the perturbed quantities depends on four free parameters, namely,the conductivity of the fluid, $\sg$, the speed-of-sound-square, $\frac{1}{3}<\left ( \frac{C_s}{c} \right )^2 \equiv \gm < 1$, which in this model may servealso as a measure of the inherent anisotropy, the GW frequency, $\om_{g}$, andthe associated angle of propagation with respect to the direction of themagnetic field, $\theta$. We find that, the GW propagation in the anisotropicmagnetized medium under consideration does excite several MHD modes, in otherwords, there is energy transfer from the gravitational to the EM degrees offreedom that could result in the acceleration of charged particles at the spotand in the subsequent damping of the GW.

Gravitational versus magnetohydrodynamic waves in curved spacetime in the presence of large-scale magnetic fields