Interaction of gravitational waves with strongly magnetized plasmas

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 specified to two different cases, first to Cartesian coordinates and a constant background magnetic fields, and second to spherical coordinates together with a background magnetic field that decays with the inverse radial distance. The equations are derived without neglecting any of the nonlinear interaction terms, and the nonlinear equations are integrated numerically. We find that for strong magnetic fields of the order of 10¹⁵  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 10²³  erg/cm³ in the case presented here, which, when assuming a relatively small volume in a star’s magnetosphere as an interaction region, can yield a total energy of at least 10⁴¹  erg and may be up to 10⁴³  erg. The absorbed energy is proportional to B₀², with B₀ the background magnetic field. The energizing of the plasma takes place on fast time scales of the order of milliseconds. Our results imply that the GW-plasma interaction is an efficient and important mechanism in magnetar atmospheres, most prominently close to the star, and, under very favorable conditions though, it might even be the primary energizing mechanism behind giant flares.