  We study the interaction of a gravitational wave (GW) with a plasma that is
strongly magnetized. The GW is considered a small disturbance, and the plasma
is modeled by the general relativistic analogue of the induction equation of
ideal MHD and the single fluid equations. The equations are derived without
neglecting any of the non-linear interaction terms, and the non-linear
equations are integrated numerically. We find that for strong magnetic fields
of the order of $10^{15} $G the GW excites electromagnetic plasma waves very
close to the magnetosonic mode. The magnetic and electric field oscillations
have very high amplitude, and a large amount of energy is absorbed from the GW
by the electromagnetic oscillations, of the order of $10^{23} $erg/cm$^3$ in
the case presented here. The absorbed energy is proportional to $B_0^2$, with
$B_0$ the background magnetic field. The energization of the plasma takes place
on fast time scales of the order of milliseconds. The amount of absorbed energy
is comparable to the energies emitted in the most energetic astrophysical
events, such as giant flares on magnetars and possibly even short Gamma ray
bursts (GRB), for which the mechanism analyzed here also has the fast
time-scales required.
