  We have performed 2.5-dimensional general relativistic magnetohydrodynamic
(MHD) simulations of the gravitational collapse of a magnetized rotating
massive star as a model of gamma ray bursts (GRBs). The current calculation
focuses on general relativistic MHD with simplified microphysics (we ignore
neutrino cooling, physical equation of state, and photodisintegration).
Initially, we assume that the core collapse has failed in this star. A few
$M_{\odot}$ black hole is inserted by hand into the calculation. The
simulations presented in the paper follow the accretion of gas into a black
hole that is assumed to have formed before the calculation begins.The
simulation results show the formation of a disk-like structure and the
generation of a jetlike outflow inside the shock wave launched at the core
bounce. We have found that the jet is accelerated by the magnetic pressure and
the centrifugal force and is collimated by the pinching force of the toroidal
magnetic field amplified by the rotation and the effect of geometry of the
poloidal magnetic field. The maximum velocity of the jet is mildly relativistic
(0.3c). The velocity of the jet becomes larger as the initial rotational
velocity of stellar matter gets faster. On the other hand, the dependence on
the initial magnetic field strength is a bit more complicated: the velocity of
the jet increases with the initial field strength in the weak field regime,
then is saturated at some intermediate field strength, and decreases beyond the
critical field strength. These results are related to the stored magnetic
energy determined by the balance between the propagation time of the Alfven
wave and the rotation time of the disk (or twisting time).
