  We have performed 2.5-dimensional general relativistic magnetohydrodynamic
(MHD) simulations of collapsars including a rotating black hole. This paper is
an extension of our previous paper (Mizuno et al. 2004). The current
calculation focuses on the effect of black hole rotation using general
relativistic MHD with simplified microphysics. Initially, we assume that the
core collapse is failed in this star. A few solar mass rotating black hole is
inserted by hand into the calculation. We consider two cases, the co-rotating
case and counter-rotating case with respect to the black hole rotation.
Although the counter-rotating case may be unrealistic for collapsar, we perform
as a maximally dragging case of magnetic field. The simulation results show the
formation of a disk-like structure and the generation of a jet-like outflow
near the central black hole. The jet-like outflow propagates outwardly with the
twisted magnetic field and becomes collimated. We have found that the jets are
generated and accelerated mainly by the magnetic field. The total jet velocity
in the rotating black hole case is comparable to that of the non-rotating black
hole case (Mizuno et al. 2004), 0.3c. When the rotation of the black hole is
faster, the magnetic field is twisted strongly owing to the frame-dragging
effect. The magnetic energy stored by the twisting magnetic field is converted
to kinetic energy of the jet directly rather than propagating as an Alfven
wave. Thus, as the rotation of the black hole becomes faster, the poloidal
velocity of the jet becomes faster. In the rapidly rotating black hole case the
jet-like outflow can be produced by the frame dragging effect only through the
twisting of magnetic field even if there is no stellar rotation.
