  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
it numerically, 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, $\sg$, the speed-of-sound-square, $\frac{1}{3}<
\left ( \frac{C_s}{c} \right )^2 \equiv \gm < 1$, which in this model may serve
also as a measure of the inherent anisotropy, the GW frequency, $\om_{g}$, and
the associated angle of propagation with respect to the direction of the
magnetic field, $\theta$. We find that, the 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 could result in the acceleration of charged particles at the spot
and in the subsequent damping of the GW.
