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.
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