  Many problems at the forefront of theoretical astrophysics require the
treatment of magnetized fluids in dynamical, strongly curved spacetimes. Such
problems include the origin of gamma-ray bursts, magnetic braking of
differential rotation in nascent neutron stars arising from stellar core
collapse or binary neutron star merger, the formation of jets and magnetized
disks around newborn black holes, etc. To model these phenomena, all of which
involve both general relativity (GR) and magnetohydrodynamics (MHD), we have
developed a GRMHD code capable of evolving MHD fluids in dynamical spacetimes.
Our code solves the Einstein-Maxwell-MHD system of coupled equations in
axisymmetry and in full 3+1 dimensions. We evolve the metric by integrating the
BSSN equations, and use a conservative, shock-capturing scheme to evolve the
MHD equations. Our code gives accurate results in standard MHD code-test
problems, including magnetized shocks and magnetized Bondi flow. To test our
code's ability to evolve the MHD equations in a dynamical spacetime, we study
the perturbations of a homogeneous, magnetized fluid excited by a gravitational
plane wave, and we find good agreement between the analytic and numerical
solutions.
