  We consider a gravitational wave oscillating in an initially homogeneous,
magnetized fluid. The fluid is perfectly conducting and isentropic, and the
magnetic field is initially uniform. We find analytic solutions for the case in
which the gravitational wave is linear and unaffected by the background fluid
and field. Our solutions show how gravitational waves can excite three
magnetohydrodynamic (MHD) modes in the fluid: Alfven waves, and both fast and
slow magnetosonic waves. Our analytic solutions are particularly useful for
testing numerical codes designed to treat general relativistic MHD in dynamical
spacetimes, as we demonstrate in a companion paper.
