  We study the magnetic interaction between a neutron star and its disk by
solving the time-dependent relativistic force-free equations. At the initial
state, we assume that the dipole magnetic field of the neutron star connects
the neutron star and its equatorial disk, which deeply enters into the
magnetosphere of the neutron star. Magnetic fields are assumed to be frozen to
the star and the disk. The rotation of the neutron star and the disk is imposed
as boundary conditions. We apply Harten-Lax-van Leer (HLL) method to simulate
the evolution of the star-disk system. We carry out simulations for (1) a disk
inside the corotation radius, in which the disk rotates faster than the star,
and (2) a disk outside the corotation radius, in which the neutron star rotates
faster than the disk. Numerical results indicate that for both models, the
magnetic field lines connecting the disk and the star inflate as they are
twisted by the differential rotation between the disk and the star. When the
twist angle exceeds pi radian, the magnetic field lines expand with speed close
to the light speed. This mechanism can be the origin of relativistic outflows
observed in binaries containing a neutron star.
