  A new implementation for magnetohydrodynamics (MHD) simulations in full
general relativity (involving dynamical spacetimes) is presented. In our
implementation, Einstein's evolution equations are evolved by a BSSN formalism,
MHD equations by a high-resolution central scheme, and induction equation by a
constraint transport method. We perform numerical simulations for standard test
problems in relativistic MHD, including special relativistic magnetized shocks,
general relativistic magnetized Bondi flow in stationary spacetime, and a
longterm evolution for self-gravitating system composed of a neutron star and a
magnetized disk in full general relativity. In the final test, we illustrate
that our implementation can follow winding-up of the magnetic field lines of
magnetized and differentially rotating accretion disks around a compact object
until saturation, after which magnetically driven wind and angular momentum
transport inside the disk turn on.
