Excitation of magnetohydrodynamic modes with gravitational waves: A testbed for numerical codes

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: Alfvén 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.